The transitions between the text and the symbols are really mesmerizing, almost satisfying lol I also learned about symbols that I have never ever used. Great video, keep it up!
Don’t worry :D math will take you step by step along the way. Also, I am sure that you will perform higher than average students based on what you chose to watch just now (or more like 3 months ago)… anyways, the point is that you are cool and epic and amazing and crazy and the bestest of the best
Kinda funny and a bit strange how he didn't explain parentheses, certain numbers and values like π, φ, θ, ε and ω, trigonometric functions, integral variations, lines and planes like ℒ and 𝒫, and more...
There aren't really many letters in the whole video, i don't think it's strange. In fact, the title says symbols and symbols ≠ letters. Also, each letter can have many many many uses so it wouldn't be as informative. Pi can be used as 3.14, in statistics (iirc pi is used for two important, different concepts) and as a constant in physics (from what i know). C can be used as the speed of light, as the little +C after every integral and probably as other things. Ive seen phi in like 5 different contexts this last semester in college. Etc. Letters would be impossible to turn into an extensive list
@@alecmartin8543to add to your list, π commonly denotes projection maps in geometry and topology, and the prime-counting function in number theory. capital C isn't actually used all that much to my knowledge, and i think that's because mathematicians like to have arbitrary constants floating around when they need them.
The video never purported to attempt to cover every single math symbol ever invented, so I don't know what you were expecting. Also, the letters θ, ε, and ω are each used for a variety of things in math. In particular, θ is most famously used as a variable for an angle measurement. Notably, this is not a particular value. My best guess is that you're talking about the ordinal numbers from set theory, but I'm really not sure.
The oplus sign (XOR) could also mean Direct Sums of groups, rings, etc. When an algebra or group is "graded", it can be decomposed into a direct sum of smaller algebras or groups.
#11 ~ can also mean (and is mainly used for) asymptoticity or arbitrary equivalence relations (as well as negation, but mostly by philosophers) #14-#17 can also be used for subgroups/subspaces/subalgebras #34 the \oplus also means, and is mainly used for, direct sums between two spaces #35 "R v ~R = T" you're setting yourself up for trouble with intuitionists lmao #49 the universal set famously doesn't exist, in case you've never heard of russell's paradox #57 "log without a subscript" is ambiguous, it depends on the surrounding discipline : in math it's usually base e (like ln), in physics it's usually base ten, and in cs it's usually base 2. #60-#61 they're more usually written Re() and Im() #62 can also be written with an * at the right side of the x, symbol which can also denote a dual space ; x̄ is also a common symbol for the average value #70 "... from on the number line" as well as in the complex plane, although it's usually called the 'modulus' there #81 damn, i've literally never seen that one ! i'd usually just write it (AB) at this point. do you have some sources that show this double combining double-ended arrow above thing being used ?
Some other uses for specific symbols: 1:17 Can be used as a relation in set theory 3:14 Right symbol can be used for a discrete change 3:28 Exterior product/wedge product 3:32 Direct sum 4:28 Almost every blackboard bold letter is used somewhere. F and K are used for fields. Blame the Germans for that one. 4:52 I have seem ' used for practically anything. Inverse of an element, complement, you name it. 5:27 Curly d is used for the boundary of something. For example, it's one of a few ways of notating the boundary in topology. 5:53 There are many different kinds of integral and variations on the symbol. For example the path integral, notated with the usual symbol with a circle on top is the integral along a closed curve. 5:43 It is more commonly used to show what an element maps to as part of a function. 6:18 Please never use mathfrak if possible. This is a personal request. 6:21 Sometimes used to represent cosets. Maybe this was just my prof? Who knows. 7:17 It can sometimes be used for any arbitrary metric, although this drives me insane. 8:00 Also can just represent any geometric vector.
Dummit & Foote's textbook uses the overbar (6:21) to denote the equivalence class of an element (cosets included), and to denote images of subgroups/subrings/submodules/subfields under a natural projection. I think I have seen at least one other text use the overbar in a similar way.
Curly braces in desmos denotes a piecewise expression in the form {condition : then, else}, not a set For example {n>3 : 7 , n+1} would evaluate to 7 if n is greater than 3, if n is not greater than 3 then it returns n+1 By default, the values for then and else are 1 and NaN (which shows up as undefined) so for example, {n>0} evaluates 1 if n>0 and NaN if n
@@cosmnik472 when you write x^2 {x>0}, desmos interprets this literally as a multiplication between x^2 and {x>0}. when x≤0, {x>0} = NaN, so multiplying by NaN gives NaN. when x>0, {x>0} = 1, so the expression is x^2 * 1= x^2, which is what needs to be plotted. so it's basically just using multiplication by 1 as the "do nothing" operation. thus, empty brackets { } denote something that is always true, so they are always equal to 1 no matter what. very cool but a little hacky in my opinion
I’m a little surprised you didn’t include the top arrow for vectors and the hat symbol for unit vectors. As a side note, physicists tend to use * for the complex conjugate and † for the Hermitian adjoint.
@@Raj_Dave They have applications in data science, programming, and pure math. The arrow notation is likely exclusive to physics, but vectors themselves are everywhere.
Arithmetic operators: plus (+), minus (-), multiplication (x or dot), division (/) Plus or minus (±) Range (-) Root symbol (√) Equal (=) Not equal (≠) Approximately equal (≈) or tilde (~) Proportionality (∝) Triple bar or equivalent (=) Less than ( Less than or equal to (≤) Greater than or equal to (≥) Much less than > Empty set symbol (∅) Number sign (#) In (∈) Not in (∉) Set inclusion (⊂) Proper subset (⊊) Union (∪) Intersection (∩) Set difference () Symmetric difference (Δ or ⊖) Negation symbol (¬) AND (&) OR (∨) XOR (⊕) True (T) False (F) Universal quantifier (∀) Existential quantifier (∃) Uniqueness quantifier (∃!) Conditional operator (→) Logical equivalence (↔) Basic number systems: N (natural numbers), Z (integers), Q (rational numbers), R (real numbers), C (complex numbers), H (quaternions), O (octonians), U (universal set) Prime (') for derivatives and dot (.) for Newton's notation Integral (∫) Function composition Logarithm (log or ln) Limit (lim) Real part (Re) Imaginary part (Im) Complex conjugate (bar over a complex number) Summation (Σ) Product (∏) Infinity (∞) Aleph (ℵ) Factorial (!) Binomial coefficient (nCk) Absolute value (|) Floor function (⌊⌋) Ceiling function (⌈⌉) Nearest integer function (round) Visibility line (-) Non-divisibility (/) Parallelism (||) Non-parallelism (∦) Perpendicularity (⊥) Coprime (/) Line segment (overline) Line or ray (→) Infinite line (↔) I hope this helps!
Now I know how to hold a brush Tho you're art is a guid without rush I am satisfied with your flow The way it is, is with no flaw Very vry nice vid BTW I am not sure how you video in the time being has 500 likes It's Strang but keep the nice work
No, that notation is used for a vector from A to B, having a certain length. I have never seen notation #81 though. I guess if you accept #81 as true, then your explanation makes more sense for #81
Sigma notation is the amount of area in a wave added infinitely to the best accuracy, like dx is base and x is height so (sigma notation) f(x) dx ( U ) is the area
2:16 In Ukrainian language there is a letter 'є'(ye) which is also a word that means "is" , it is quite interesting how close it is to the mathematical meaning of that symbol.
5:31 the integral isn’t necessarily an antiderivative but the difference between 2 anti derivatives can be a shortcut to finding the integral the integral is the sum of all outcomes of a function between a upper and lower limit (think of sigma but not limited to integers)
Sure! Here’s a list of 81 math symbols and their meanings: 1. **+** - Addition 2. **-** - Subtraction 3. **×** - Multiplication 4. **÷** - Division 5. **=** - Equals 6. **≠** - Not equal to 7. **** - Greater than 9. **≤** - Less than or equal to 10. **≥** - Greater than or equal to 11. **±** - Plus or minus 12. **∓** - Minus or plus 13. **√** - Square root 14. **∛** - Cube root 15. **∜** - Fourth root 16. **^** - Exponentiation (e.g., x^y) 17. **π** - Pi 18. **e** - Euler's number 19. **i** - Imaginary unit (√-1) 20. **Σ** - Summation 21. **Π** - Product 22. **∫** - Integral 23. **∂** - Partial derivative 24. **∇** - Del (nabla), gradient 25. **∞** - Infinity 26. **≈** - Approximately equal to 27. **≡** - Identically equal to 28. **⊂** - Subset 29. **⊃** - Superset 30. **∈** - Element of 31. **∉** - Not an element of 32. **∪** - Union 33. **∩** - Intersection 34. **∅** - Empty set 35. **|A|** - Cardinality of set A 36. **⊥** - Perpendicular 37. **∠** - Angle 38. **∥** - Parallel 39. **∝** - Proportional to 40. **∴** - Therefore 41. **∵** - Because 42. **⨁** - Direct sum 43. **⨂** - Tensor product 44. **⊕** - Direct sum or exclusive or (XOR) 45. **⊗** - Tensor product 46. **⨉** - Cartesian product 47. **∧** - Logical and 48. **∨** - Logical or 49. **¬** - Logical negation 50. **⇒** - Implies 51. **⇔** - If and only if 52. **∀** - For all 53. **∃** - There exists 54. **∄** - There does not exist 55. **∧** - Logical conjunction (and) 56. **∨** - Logical disjunction (or) 57. **⊥** - Orthogonality 58. **∧** - Logical and 59. **∨** - Logical or 60. **⇒** - Implies 61. **⇔** - If and only if 62. **∅** - Empty set 63. **↔** - Bi-conditional 64. **⊥** - Perpendicular 65. **⊤** - True 66. **⊥** - False 67. **Δ** - Delta (change) 68. **θ** - Theta (angle or variable) 69. **α** - Alpha (angle or coefficient) 70. **β** - Beta (angle or coefficient) 71. **γ** - Gamma (angle or coefficient) 72. **ρ** - Rho (density or correlation coefficient) 73. **σ** - Sigma (standard deviation) 74. **τ** - Tau (time constant) 75. **λ** - Lambda (wavelength or eigenvalue) 76. **ζ** - Zeta (damping ratio) 77. **φ** - Phi (golden ratio or angle) 78. **χ** - Chi (chi-square) 79. **ψ** - Psi (wave function or angle) 80. **Ω** - Omega (last in a series or angular velocity) 81. **Ξ** - Xi (random variable or matrix) These symbols cover a wide range of mathematical concepts, from basic operations to more advanced topics. If you need explanations for specific symbols or additional details, let me know!
Air detected! Water on the hill! Fire in the hole! Area confirmed! Rock on the ground! Wind from the landscape! Lightning on the road! Bees from the hive! Kids at the basement! Magma in the bound! Blood in the bath! Wait no I hate lobotomy 💀
imo these are just letters, not special mathematical symbols. thus that is not "an unforgivable crime". it is like saying the author should have added the whole latin alphabet only because mathematicians tend to use it moreover, the preferrable usage of *letters* in mathematics highly depend on a country. For instance, google claims the letter for "area" is "A", but we in eastern europe are likely to use "S" suppose you did not try thinking before posting your comment 😀
@@tyrjialBro took a damn yt comment serious💀 No he's just tryna say that like if you think of math π is one of the first things that come to your mind, oretty important to math
I remember once in math class when i was supposed to draw lines to indicate how many parts circle can be sheard and the last circle was supposed to shear with any number of lines i wanted to indicate infinite shearing. Instead of lines i simply drew the infinity symbol and my teacher was a bit surprised. Not that i was wrong about my answer, but he/she didn't expect such clever answer coming from so young boy i was back then. One of my funniest memmories from elementary school.😆😊
Very interesting seeing the logic philosophy symbols, learned that last semester and didn’t know if they actually counted as a math symbols lol. Haven’t seen it anywhere else.
1:15 Tilda would have been nice to know back in 5th grade when the teacher told us you weren't done with your answer and could be reduced down. Tilda would have been awesome to use. 4π/6~2π/3
"sigma" Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head Get out of my head
Math is a language, and often the symbols are still up to interpretation. ✖️is used for multiplying numbers, cross-products on vectors, cartesian/ direct products on sets, and likely has some more applications (ie. Field Theory/ Ring Theory) Symbols are usually representative of Relations, whereas we often describe theoretical relations with dummy-symbols: “A relation R relates elements from the structure S, such that for all x,y of S: xRy” - and we would give properties to R, such as defining Reflexivity, Symmetry, and Transitivity,,, which are necessary properties for defining Equality and Ordering. Ordering is described in books using ambiguous symbols, but the convention is well documented- literally, a “partial order” is typically given a < symbol (sometimes it looks more squiggly),,, this is because < behaves pretty much the exact same way (not technically). Numerals themselves, I believe, are / are related to Quantifiers. Instead of “For All” or “There exist” etc 4 = “Four” - is a symbolic representation of a quantity. One of the topics I study tries to recognize that numerals represent quantities, which allows us to use numbers to define Abstract concepts- knowing that Scalars are Tensors that are built on those concepts (so, I try to unwrap the paradoxes) ~ is also used for logical negations (predicate logic), is probably more common. Predicates, in my opinion are just one type of logical statement, and the behavior comes from their ancestors… But, it is arguably a linguistics topic that intersects math (not my expertise) # is sometimes used instead of R for relations- I’ve also seen it used in Topology as an operation for “gluing manifolds”,,, but idk anything about that subject. FunFact: The Union and Intersect symbols are used for set operations - they are also used for Families, with a slightly different notation (I forget which definition for “Family”,,, as it can mean many things)
7:59 No, it represents a ray with an endpoint at the first point and passing through the second, going off toward infinity. A ray does not have two endpoints.
It's not rigorously defined, but it can be useful when the exact numbers are not really important, only their magnitudes. For example, you could be discussing the non-associativity of exponentiation and state 3^(3^3) >> (3^3)^3. This puts emphasis on the fact that we get a much larger value when evaluating right to left as opposed to left to right. You could use a normal > sign, but then you're losing that emphasis. In some rare occasions, you can even see more symbols added to denote extreme differences in magnitude (for example, TREE(3) >>> Graham's Number).
Mathematics fact : you can represent a complex number by x+iy where x is the real part and y is the imaginary part. A sq root of a negative number will be a complex number. Where i⁰ is 1 and i¹ is i and i² is -1 if you plot it on graph you will get a circle of radius pi.
+ =plus sing - =minus sing × =multiplication sing ÷ =division sing ± =plus minus sing √ =square root symbol ≠ =not=equal sing ≈ =approximately equal sing ~ =similarity/proportionality ∝ =proportionality ≡ =tripel bar < =Less-than sing > =Greater-than sing ≤ =Less than or equal ≥ =Greater than or equal « =much Less than » =much Greater than ∅ =empty set # =number sing ⊂ =set inclusion ∪ =union ∩ =intersection \ =difference I can only do this much Thank you for reading
My mental stage: "This is basic stuff I know" "Ooo, I know this one!" "Oh, so what that means" "Uh, what?" "What" "huh?" "Oh, I learned this" "I don't know this" " I've never learned this" "I've never seen this" "I know this! This is my project" 'uhhh" "Uhmm" "..."
3:15 btw triangle can be seen as the letter Delta from the greek alphabet, and the other one is Theta. (also from the greek alphabet) Delta is also usually used as the change of something. and theta im pretty sure equals rotation of a circle/circumference or just rotation, i dont know anything else
Now I understand that the math language also has a lot of dialects..
Math exists because of determinism i think, if we didnt have need to simplify and to count, would we invent it.
Imagine 19th century mathematicians trying to standardize these things
@@moumdohthey did not do well
Fr
@@chri-kBecause there’s too many operations to have consistency in the movement of symbols
0:02 Plus
0:06 Minus
0:15 Multiply
0:20 Divide
0:25 Plus-Minus
0:32 Minus-Plus
0:47 Sqr. Root
0:55 Equals Sign
1:04 Not Equals Sign
1:09 Approx. Equals sign
1:17 Tilda
1:21 Proport.
1:25 Triple Bar
1:34 Less Than
1:40 Greater Than
1:46 Less/Equal
1:54 Greater/Equal
1:59 M. Less
2:01 M. Gre
2:05 Empty Set
2:08 Number
2:16 Membership
2:21 No membership
2:24 Inclusion
2:28 emph. Set inclusion
2:37 Proper subset
2:41 Union
2:49 Intersection
2:57 Difference
3:07 Symmetric Diff.
3:17 Negation
3:24 Or
3:27 And
3:31 Exc. Or
3:36 Tee
3:41 Up Tack
3:48 Un. Quant.
3:52 Ex. Quant.
4:00 Unique Quant.
4:08 Implied
4:16 Logical Equi.
4:22 Blackboard Bold Typeface
4:26 N
4:29 Z
4:31 Q
4:33 R
4:35 C
4:38 H
4:40 O
4:43 U
4:48 Lag. Not.
4:50 Der. Of f
5:00 Newt. Not.
5:01 Der. of var X
5:14 Lieb Not. Der of f with respect
5:23 Part. Der of f
5:28 Integral
5:43 Arrow
5:50 Func. Comp.
5:54 log
6:02 ln
6:09 lim
6:12 Fancy R
6:17 Fancy I
6:20 bar above complex
6:29 Sigma Func.
6:33 Capital Pi Func.
6:40 Infinity
6:45 Aleph
6:53 Fraktur C
6:59 Factorial
7:02 Bin. Coeff.
7:14 absolute value
7:21 floor
7:24 ceiling
7:30 near. int. func.
7:36 divisibility
7:41 no divisibility
7:41 parallel
7:46 not parallel
7:47 perp/coprime
7:56 line seg.
8:00 ray
8:05 inf. line
Thank you for your service 🫡
are you unemployed
What the sigma func.?
@@mahesh-x7w uh ya why??
Erm what the sigma
π, ∆, °, %, ∠, ∮, Nabla, and many more, but still most of the topics covered
π: 3.1415926535897932384626433832795
∆: Discriminant
°: Degree
%: Percent
∠: Angle
∮: Contour integral (of a vector field)
∇: Gradient
U
@@AlbertTheGamer-gk7snw
pi isn’t really a mathematical symbol. it’s a number that happens to have a symbol associated with it
This video just covers anything high school. Anything more than that is primarily used by people who don't need these videos
6:29
I can never see this the same after what my class has done to it.
Edit: Day by day I regret making this comment.
I know!
Ikr😅
Erm, what the sigma
Such a great math symbol and greek letter, it didnt deserve to get treated like this
@@Seagullguy144bro
3:18
Note for the logic symbols, it is also common to see negation as a line over a term, AND as multiplication, and OR as addition.
In my introductory math logic class we wrote negation as a tilde (~P)
true , the AND sign is also used for greatest common divisor and OR sign for lowest common multiple
Math is like a video game, the more you level up, the more symbols or characters unlock.
Wow! This is by far the best mathematic proverb! Congratulations!
Mathio kart
this is a tutorial to unlock them all
why does this relate to me?🤔🤔
Similar thought unfolded in WarioWare Gold
Math is like meth, once you start using it properly you can't stop it
Dang.
Methimatics
Lionel Methi
Relatable
so thats why they show it like a minus sign...
The transitions between the text and the symbols are really mesmerizing, almost satisfying lol
I also learned about symbols that I have never ever used. Great video, keep it up!
The most underrated math channel ever, even if you've already started blowing up
I'm probably the #2 most underrated math channel then
It's not, because there's not a Skibidi Toilet math thing
As a person whos about to finish elementary school my brain is turning into popcorn.
And you used caps and at least one punctuation, but probably ignored the suggestions from you keyboard for the rest. Maybe there is hope.
Don’t worry :D math will take you step by step along the way. Also, I am sure that you will perform higher than average students based on what you chose to watch just now (or more like 3 months ago)… anyways, the point is that you are cool and epic and amazing and crazy and the bestest of the best
@@jordythesheep Thanks!
you saw Sigma in the thumbnail and clicked it, didn't you?
@@Redlightsy People expect so much out of us nowadays, all i wanted to do was learn are you out of your mind?
Kinda funny and a bit strange how he didn't explain parentheses, certain numbers and values like π, φ, θ, ε and ω, trigonometric functions, integral variations, lines and planes like ℒ and 𝒫, and more...
I would have liked if he went into a bit more depth on the aleph notations but the editing must have taken a lot of work already
There aren't really many letters in the whole video, i don't think it's strange. In fact, the title says symbols and symbols ≠ letters. Also, each letter can have many many many uses so it wouldn't be as informative. Pi can be used as 3.14, in statistics (iirc pi is used for two important, different concepts) and as a constant in physics (from what i know). C can be used as the speed of light, as the little +C after every integral and probably as other things. Ive seen phi in like 5 different contexts this last semester in college. Etc. Letters would be impossible to turn into an extensive list
@@alecmartin8543to add to your list, π commonly denotes projection maps in geometry and topology, and the prime-counting function in number theory. capital C isn't actually used all that much to my knowledge, and i think that's because mathematicians like to have arbitrary constants floating around when they need them.
@@alecmartin8543Letters are absolutely symbols.
The video never purported to attempt to cover every single math symbol ever invented, so I don't know what you were expecting.
Also, the letters θ, ε, and ω are each used for a variety of things in math. In particular, θ is most famously used as a variable for an angle measurement. Notably, this is not a particular value. My best guess is that you're talking about the ordinal numbers from set theory, but I'm really not sure.
WHERE WERE YOU WHEN I WAS DOING MY BACHELOR'S IN MATH YOU WOULD HAVE HELPED ME THROUGH SO MUCH CONFUSION
This is an obvious lie
The oplus sign (XOR) could also mean Direct Sums of groups, rings, etc. When an algebra or group is "graded", it can be decomposed into a direct sum of smaller algebras or groups.
I'm a math grad student and i have never seen it used for XOR lmao
@@TepsiMorphic Agreed HAHAHAHAHAHAH
#11 ~ can also mean (and is mainly used for) asymptoticity or arbitrary equivalence relations (as well as negation, but mostly by philosophers)
#14-#17 can also be used for subgroups/subspaces/subalgebras
#34 the \oplus also means, and is mainly used for, direct sums between two spaces
#35 "R v ~R = T" you're setting yourself up for trouble with intuitionists lmao
#49 the universal set famously doesn't exist, in case you've never heard of russell's paradox
#57 "log without a subscript" is ambiguous, it depends on the surrounding discipline : in math it's usually base e (like ln), in physics it's usually base ten, and in cs it's usually base 2.
#60-#61 they're more usually written Re() and Im()
#62 can also be written with an * at the right side of the x, symbol which can also denote a dual space ; x̄ is also a common symbol for the average value
#70 "... from on the number line" as well as in the complex plane, although it's usually called the 'modulus' there
#81 damn, i've literally never seen that one ! i'd usually just write it (AB) at this point. do you have some sources that show this double combining double-ended arrow above thing being used ?
Some other uses for specific symbols:
1:17 Can be used as a relation in set theory
3:14 Right symbol can be used for a discrete change
3:28 Exterior product/wedge product
3:32 Direct sum
4:28 Almost every blackboard bold letter is used somewhere. F and K are used for fields. Blame the Germans for that one.
4:52 I have seem ' used for practically anything. Inverse of an element, complement, you name it.
5:27 Curly d is used for the boundary of something. For example, it's one of a few ways of notating the boundary in topology.
5:53 There are many different kinds of integral and variations on the symbol. For example the path integral, notated with the usual symbol with a circle on top is the integral along a closed curve.
5:43 It is more commonly used to show what an element maps to as part of a function.
6:18 Please never use mathfrak if possible. This is a personal request.
6:21 Sometimes used to represent cosets. Maybe this was just my prof? Who knows.
7:17 It can sometimes be used for any arbitrary metric, although this drives me insane.
8:00 Also can just represent any geometric vector.
7:17 It is used as a symbol for determinants too.
Dummit & Foote's textbook uses the overbar (6:21) to denote the equivalence class of an element (cosets included), and to denote images of subgroups/subrings/submodules/subfields under a natural projection. I think I have seen at least one other text use the overbar in a similar way.
The bar can be used for the absolute of a value, the determinant of a matrix, the magnitude of a vector, the cardinality of a set, maybe more 🤷♂️
Thanks for the video, it helped me learn calculus, logic, sets and logarithm at 12
you been really helpful till now ,
have a nice day man
Which number are you talking about which is greater than 3, 2 or 1 or between??
aleph sighted watch out for abnormalities
project moon sleeper agents activate
ALEPH?? ALEPH CLASS???? LIKE AS IN ALEPH FROM LOOBOTOMY CORPORATION??? HOLY SHIT! LOBOTOMY CORPIRATION MENTIONED!
As a person being forced to learn hebrew, i kinda went like what when i found out hebrew pulled up to math
I knew there was going to be a PM comment here
anyways, SLEEPER AGENTS ACTIVATED!!!!!!!!!!!!!!!!
I can barely wait for a "FrEe PaLeStInE" comment
I learnt all of these the hard way, this is a good video for beginner in math notation
Symbol list:
-Plus sign (+)
-Minus sign (-)
-Multiplication sign (x or .)
-Division sign (÷)
-Plus-minus sign (±)
-Minus-plus sign (∓)
-Square root symbol (√)
-Equal sign (=)
-Not-equal sign (≠)
-Approximately equal sign (≈)
-Similarity/proportionality (~)
-Proportionality (∝)
-Triple bar (≡)
-Less-than sign ()
-Less than or equal (≤)
-Greater than or equal (≥)
-Much less than sign (≪)
-Much greater than sign (≫)
-Empty set symbol (Ø)
-Number sign (#)
-Set inclusion sign (⊂)
-Equal set inclusion (⊆)
-Not equal set inclusion (⊈)
-Union (⋃)
-Intersection (⋂)
-Difference (\)
-Symmetric difference (⊖ or △)
-Or (∨)
-And (∧)
-Exclusive or (⊕)
-Tee (T)
-Up tack (⊥)
-Universal quantifer (∀)
-Existential quantiner (Ǝ)
sin(θ) ≡ ℑ(e^iθ)
cos(θ) ≡ ℜ(e^𝔦θ)
These two letters have absolutely NO NEED to be doing all that 😂
Bro type in English I can't understand
@@niceboiiz learn satanic
@@jskkdjjekam no I have to learn trigonometry
You're wrong.
sin(i)≈1.175i
Im(e^(i×i))=Im(1/e)=0
All the ipad kids are getting hyped at 6:29 no cap 💀🤚
Empty sets in Desmos have the value of 1 [ WHAT?! ]
Curly braces in desmos denotes a piecewise expression in the form {condition : then, else}, not a set
For example {n>3 : 7 , n+1} would evaluate to 7 if n is greater than 3, if n is not greater than 3 then it returns n+1
By default, the values for then and else are 1 and NaN (which shows up as undefined) so for example, {n>0} evaluates 1 if n>0 and NaN if n
Fr
@@cosmnik472 when you write x^2 {x>0}, desmos interprets this literally as a multiplication between x^2 and {x>0}. when x≤0, {x>0} = NaN, so multiplying by NaN gives NaN. when x>0, {x>0} = 1, so the expression is x^2 * 1= x^2, which is what needs to be plotted. so it's basically just using multiplication by 1 as the "do nothing" operation. thus, empty brackets { } denote something that is always true, so they are always equal to 1 no matter what. very cool but a little hacky in my opinion
@@cosmnik472 As someone who uses desmos i couldnt appreciate your reply more
But got some reason, {} = 1
B:
The lower the number, the bigger it gets.
1/0 [base integer / zero possibilities -> infinite possibilities]
1/0=inf
I’m a little surprised you didn’t include the top arrow for vectors and the hat symbol for unit vectors.
As a side note, physicists tend to use * for the complex conjugate and † for the Hermitian adjoint.
Aren't vectors a physics concept?
@@Raj_Dave They have applications in data science, programming, and pure math. The arrow notation is likely exclusive to physics, but vectors themselves are everywhere.
Please explain also with the symbols based numerical examples I am waiting 😊 👍🏻 nice and Informative videos thank you sir
Arithmetic operators: plus (+), minus (-), multiplication (x or dot), division (/)
Plus or minus (±)
Range (-)
Root symbol (√)
Equal (=)
Not equal (≠)
Approximately equal (≈) or tilde (~)
Proportionality (∝)
Triple bar or equivalent (=)
Less than (
Less than or equal to (≤)
Greater than or equal to (≥)
Much less than >
Empty set symbol (∅)
Number sign (#)
In (∈)
Not in (∉)
Set inclusion (⊂)
Proper subset (⊊)
Union (∪)
Intersection (∩)
Set difference ()
Symmetric difference (Δ or ⊖)
Negation symbol (¬)
AND (&)
OR (∨)
XOR (⊕)
True (T)
False (F)
Universal quantifier (∀)
Existential quantifier (∃)
Uniqueness quantifier (∃!)
Conditional operator (→)
Logical equivalence (↔)
Basic number systems: N (natural numbers), Z (integers), Q (rational numbers), R (real numbers), C (complex numbers), H (quaternions), O (octonians), U (universal set)
Prime (') for derivatives and dot (.) for Newton's notation
Integral (∫)
Function composition
Logarithm (log or ln)
Limit (lim)
Real part (Re)
Imaginary part (Im)
Complex conjugate (bar over a complex number)
Summation (Σ)
Product (∏)
Infinity (∞)
Aleph (ℵ)
Factorial (!)
Binomial coefficient (nCk)
Absolute value (|)
Floor function (⌊⌋)
Ceiling function (⌈⌉)
Nearest integer function (round)
Visibility line (-)
Non-divisibility (/)
Parallelism (||)
Non-parallelism (∦)
Perpendicularity (⊥)
Coprime (/)
Line segment (overline)
Line or ray (→)
Infinite line (↔)
I hope this helps!
Thanks for the best abstract in Mathematics. 👌👍
This brings joy to my heart. Thanks for making this video :D
#34 is also used for direct sum of modules in linear algebra
In the starting, It was a maths video but in the end it a great grand IIT professor explaining computer language....
6:31 ayo were talking about gen z🗣️
Edit: thanks for 45 likes MOM IM FAMIUS
“Gen alpha”
Also sigma should only be used on math not some stupid ass slang
I have the “sigma”
Yeah really right @@Trollgesolosevilnungoons
It's just a sequence
Now I know how to hold a brush
Tho you're art is a guid without rush
I am satisfied with your flow
The way it is, is with no flaw
Very vry nice vid
BTW I am not sure how you video in the time being has 500 likes
It's Strang but keep the nice work
your*
Our teacher taught us that the '±' can also be used to say 'or more' as in:
It was around 50± = it was around fifty or more
small correction for #80: the ray starts at the first point and PASSES THROUGH the second point, rather than ending at it.
BADA *BING*
No, that notation is used for a vector from A to B, having a certain length. I have never seen notation #81 though. I guess if you accept #81 as true, then your explanation makes more sense for #81
@@skylardeslypere9909 BADA *BOOM*
@@TheDoc-Worker lol
Sigma notation is the amount of area in a wave added infinitely to the best accuracy, like dx is base and x is height so (sigma notation) f(x) dx ( U ) is the area
Those who know 💀
@SomebodyAteMyCookies wdym
@@GospelSpreader123 It's a brain rot thing nevermind
2:16 In Ukrainian language there is a letter 'є'(ye) which is also a word that means "is" , it is quite interesting how close it is to the mathematical meaning of that symbol.
you have an incredible talent for making complex topics simple!
5:31 the integral isn’t necessarily an antiderivative
but the difference between 2 anti derivatives can be a shortcut to finding the integral
the integral is the sum of all outcomes of a function between a upper and lower limit (think of sigma but not limited to integers)
That would be a definite integral, an indefinite is still just an antiderivative
@@ahasdasetodu6304 kk
Great video man. Lost track at like 6 minutes into the video but still a great high-quality and definitely useful for now and the future video. 🙏
Instructions unclear, my brain is now in meth
Sure! Here’s a list of 81 math symbols and their meanings:
1. **+** - Addition
2. **-** - Subtraction
3. **×** - Multiplication
4. **÷** - Division
5. **=** - Equals
6. **≠** - Not equal to
7. **** - Greater than
9. **≤** - Less than or equal to
10. **≥** - Greater than or equal to
11. **±** - Plus or minus
12. **∓** - Minus or plus
13. **√** - Square root
14. **∛** - Cube root
15. **∜** - Fourth root
16. **^** - Exponentiation (e.g., x^y)
17. **π** - Pi
18. **e** - Euler's number
19. **i** - Imaginary unit (√-1)
20. **Σ** - Summation
21. **Π** - Product
22. **∫** - Integral
23. **∂** - Partial derivative
24. **∇** - Del (nabla), gradient
25. **∞** - Infinity
26. **≈** - Approximately equal to
27. **≡** - Identically equal to
28. **⊂** - Subset
29. **⊃** - Superset
30. **∈** - Element of
31. **∉** - Not an element of
32. **∪** - Union
33. **∩** - Intersection
34. **∅** - Empty set
35. **|A|** - Cardinality of set A
36. **⊥** - Perpendicular
37. **∠** - Angle
38. **∥** - Parallel
39. **∝** - Proportional to
40. **∴** - Therefore
41. **∵** - Because
42. **⨁** - Direct sum
43. **⨂** - Tensor product
44. **⊕** - Direct sum or exclusive or (XOR)
45. **⊗** - Tensor product
46. **⨉** - Cartesian product
47. **∧** - Logical and
48. **∨** - Logical or
49. **¬** - Logical negation
50. **⇒** - Implies
51. **⇔** - If and only if
52. **∀** - For all
53. **∃** - There exists
54. **∄** - There does not exist
55. **∧** - Logical conjunction (and)
56. **∨** - Logical disjunction (or)
57. **⊥** - Orthogonality
58. **∧** - Logical and
59. **∨** - Logical or
60. **⇒** - Implies
61. **⇔** - If and only if
62. **∅** - Empty set
63. **↔** - Bi-conditional
64. **⊥** - Perpendicular
65. **⊤** - True
66. **⊥** - False
67. **Δ** - Delta (change)
68. **θ** - Theta (angle or variable)
69. **α** - Alpha (angle or coefficient)
70. **β** - Beta (angle or coefficient)
71. **γ** - Gamma (angle or coefficient)
72. **ρ** - Rho (density or correlation coefficient)
73. **σ** - Sigma (standard deviation)
74. **τ** - Tau (time constant)
75. **λ** - Lambda (wavelength or eigenvalue)
76. **ζ** - Zeta (damping ratio)
77. **φ** - Phi (golden ratio or angle)
78. **χ** - Chi (chi-square)
79. **ψ** - Psi (wave function or angle)
80. **Ω** - Omega (last in a series or angular velocity)
81. **Ξ** - Xi (random variable or matrix)
These symbols cover a wide range of mathematical concepts, from basic operations to more advanced topics. If you need explanations for specific symbols or additional details, let me know!
waiting for a kid to say "OmG gUyS lOoK iTs sIgMa!!! wHeN aRe We GeTtInG sKiBidI??!??"
Sigma is summation
Yeah. There's Sigma at 6:30 but not Skibidi
when we getting wolf
If they have a fancy pc he could flex with the symbol Σ
Thank You so much for this video. I am making a book and all this info is helping me out a lot. Will share when done to you
6:29 When the Brainrot takes over Math
Bruh
The sigma symbol was used for summation, way before this slang came out. Think before you joke.
I KNEW SOME *DUMB* *KID* WOULD COMMENT THAT
Air detected! Water on the hill! Fire in the hole! Area confirmed! Rock on the ground! Wind from the landscape! Lightning on the road! Bees from the hive! Kids at the basement! Magma in the bound! Blood in the bath!
Wait no I hate lobotomy 💀
eat
Part 1:
Plus sign ( + )
5 + 4 = 9
Minus sign ( - )
7 - 4 = 3
-4, -2, -7
Multiplication sign ( × or • )
3 × 7 = 21
3 • 7 = 21
Divison sign ( ÷ or / or : )
21 ÷ 7 = 3
21 / 7 = 3
21 : 7 = 3
Plus-minus sign ( + or - )
5 + or - 3 = 8 or 2
Minus-plus sign ( - or + )
_a_ + or - _b_ - or + _c_ = _a_ + _b_ - _c_ or _a_ - _b_ + _c_
_a_ + or - _b_ - or + _c_ ≠ _a_ - _b_ - _c_ or _a_ + _b_ + _c_
Square root symbol ( √ )
√ _x_ = square root of _x_
_n_ √ _x_ = _n_ th root of _x_
Equals sign ( = )
3 + 2 = 5
37 = 37
_a_ + 1 = _a_ + 1
Not-equal sign ( ≠ )
3 + 2 ≠ 6
37 ≠ 36
_a_ + 1 ≠ _a_ - 1
Approximately equal sign ( ≈ )
3 + 2 ≈ 4.99
37 ≈ 37.1
_a_ + 1 ≈ _a_ + 1.0001
Thank you so much!!! your content is so heplful
6:20 The complex conjugate of a number z can also be denoted z*
0:54 ah yes the plus sign written as "="
Is bro deaf....
Yes
"+" may also be used to denote that the operation requires the use of a Phillips head screwdriver.
Apparently you have to be Canadian to appreciate that joke, meanwhile happy Canada day
Not adding π, iota, theta is unforgivable.
imo these are just letters, not special mathematical symbols. thus that is not "an unforgivable crime". it is like saying the author should have added the whole latin alphabet only because mathematicians tend to use it
moreover, the preferrable usage of *letters* in mathematics highly depend on a country. For instance, google claims the letter for "area" is "A", but we in eastern europe are likely to use "S"
suppose you did not try thinking before posting your comment 😀
@@tyrjialBro took a damn yt comment serious💀
No he's just tryna say that like if you think of math π is one of the first things that come to your mind, oretty important to math
And exponential!
Theta = Θ, Iota = ι
that's just kidding
I remember once in math class when i was supposed to draw lines to indicate how many parts circle can be sheard and the last circle was supposed to shear with any number of lines i wanted to indicate infinite shearing. Instead of lines i simply drew the infinity symbol and my teacher was a bit surprised. Not that i was wrong about my answer, but he/she didn't expect such clever answer coming from so young boy i was back then. One of my funniest memmories from elementary school.😆😊
-sees sigma-
-sighs-
-checks comment section-
Very interesting seeing the logic philosophy symbols, learned that last semester and didn’t know if they actually counted as a math symbols lol. Haven’t seen it anywhere else.
Thank you so much, I have always wanted to know these symbols.
1:15
Tilda would have been nice to know back in 5th grade when the teacher told us you weren't done with your answer and could be reduced down.
Tilda would have been awesome to use. 4π/6~2π/3
6:59 also omega represents 2nd.
Twenty-fourth or last.
"sigma"
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6:44 LOBOTOMY CORP YEAAAÁA
I AM FUCKING TIRED OF PROJECTMOON BRAINROT GET OUT OF MY HEAD GET OUT OF MY HEAD GET OUT OF MY HEAD
@@spine_being project moon my beloved
@@spine_being at least it's not sigma or whatever the fuck brainrot is these days
Math is a language, and often the symbols are still up to interpretation.
✖️is used for multiplying numbers, cross-products on vectors, cartesian/ direct products on sets, and likely has some more applications (ie. Field Theory/ Ring Theory)
Symbols are usually representative of Relations, whereas we often describe theoretical relations with dummy-symbols:
“A relation R relates elements from the structure S, such that for all x,y of S: xRy” - and we would give properties to R,
such as defining Reflexivity, Symmetry, and Transitivity,,, which are necessary properties for defining Equality and Ordering.
Ordering is described in books using ambiguous symbols, but the convention is well documented- literally, a “partial order” is typically given a < symbol (sometimes it looks more squiggly),,, this is because < behaves pretty much the exact same way (not technically).
Numerals themselves, I believe, are / are related to Quantifiers. Instead of “For All” or “There exist” etc 4 = “Four” - is a symbolic representation of a quantity.
One of the topics I study tries to recognize that numerals represent quantities, which allows us to use numbers to define Abstract concepts- knowing that Scalars are Tensors that are built on those concepts (so, I try to unwrap the paradoxes)
~ is also used for logical negations (predicate logic), is probably more common. Predicates, in my opinion are just one type of logical statement, and the behavior comes from their ancestors… But, it is arguably a linguistics topic that intersects math (not my expertise)
# is sometimes used instead of R for relations- I’ve also seen it used in Topology as an operation for “gluing manifolds”,,, but idk anything about that subject.
FunFact: The Union and Intersect symbols are used for set operations - they are also used for Families, with a slightly different notation (I forget which definition for “Family”,,, as it can mean many things)
the sign 'sigma'
There are so many missing, but I am happy that I got to learn so e new ones to the very least.
Aleph is a Hebrew letter 6:50
Aleph is a Hebrew letter 6:50
Aleph is a Hebrew letter 6:50
Aleph is a Hebrew letter 6:50
1) 1+1=2
2) 1-1=0
3) 1×4=4
4) 1÷3=1
5) 3±4=-1 / (or 7)
6) 3+2≈4.99
7) sin² x+cos²≡1
(a+b)²≡a²+2ab+b²
8) 53
imaginary? are you kidding me? They couldn’t cope with their math being wrong so they just made imaginary numbers
The funny thing is that you're not exactly wrong.
it makes math cooler tho sooo
They couldn't cope with x + 2 = 0 having no solution so they just made negative numbers :D
Real
i^2 = -1, j^4 = -1, and k^6 = -1
I usually think of the - sign as only representing negative numbers because subtraction is just addition of negative numbers when you think about it
ermmm what the Σ?
erhmmmm.... what the fuck?
Erm what the actual sum?
1:55 1:55 1:55 1:55
😂😂😂😂😂😂
its called 'sigma'
Shit got real after the divide sign
Sigma 💀
how old are you?
7:59 No, it represents a ray with an endpoint at the first point and passing through the second, going off toward infinity. A ray does not have two endpoints.
Welp guys, he said sigma. Are we awaiting brainrots to finnaly learn something?
erm what the sigma
Sigma is not brainrot it is a mindset to achieve success
“brainrots”? Lol.
Sigma is math
The equal sign was created very recently (relatively). Before the sign was created. PPL used to write. "is equal to"
1:56 but what is the criteria for using these symbols, i mean, when does "less than" become "much less than" and what is the use of noting that?
It's not rigorously defined, but it can be useful when the exact numbers are not really important, only their magnitudes. For example, you could be discussing the non-associativity of exponentiation and state 3^(3^3) >> (3^3)^3. This puts emphasis on the fact that we get a much larger value when evaluating right to left as opposed to left to right. You could use a normal > sign, but then you're losing that emphasis. In some rare occasions, you can even see more symbols added to denote extreme differences in magnitude (for example, TREE(3) >>> Graham's Number).
what about a very much less than and very much greater than symbols
i was just about to say the same thing!
Amazing. Now we need this kind of videos for other languages like programming languages etc.
0:24 Serbs write it with a colon :
I love gd cologn
(I was thinking the same thing)
Poles also do it
And he was saying: “It sometimes written as a colon”
@@KadziYTEspecially with that “normal face” PFP.
Same (im from Russia)
Sigma: normal
Sigma:🗿
Sigma is a letter in the Greek alphabet
2:58 In our math class, we use minus sign instead of backslash in set difference.
Same, I think you are somewhere in Asia. Correct me if I'm wrong tho
Now the sigma simbol got me☠️☠️☠️☠️☠️☠️☠️
Mathematics fact : you can represent a complex number by x+iy where x is the real part and y is the imaginary part. A sq root of a negative number will be a complex number. Where i⁰ is 1 and i¹ is i and i² is -1 if you plot it on graph you will get a circle of radius pi.
0:25 real sigmas use x over y
Alphas use β1/β2
@@BrokenBattle tangents use sin/cos
@@SpeedyMcMichael big numbers use ^/e
+ =plus sing
- =minus sing
× =multiplication sing
÷ =division sing
± =plus minus sing
√ =square root symbol
≠ =not=equal sing
≈ =approximately equal sing
~ =similarity/proportionality
∝ =proportionality
≡ =tripel bar
< =Less-than sing
> =Greater-than sing
≤ =Less than or equal
≥ =Greater than or equal
« =much Less than
» =much Greater than
∅ =empty set
# =number sing
⊂ =set inclusion
∪ =union
∩ =intersection
\ =difference
I can only do this much
Thank you for reading
primary school kid:💀💀💀
My mental stage:
"This is basic stuff I know"
"Ooo, I know this one!"
"Oh, so what that means"
"Uh, what?"
"What"
"huh?"
"Oh, I learned this"
"I don't know this"
" I've never learned this"
"I've never seen this"
"I know this! This is my project"
'uhhh"
"Uhmm"
"..."
6:30 Gen alpha ruined this one
Maths is like a story, as the story progresses new characters and elements are introduced
9² math symbols explained
Sqrt(81) = x - > x ( 2 ) math symbols solved
What (7!÷sqrt(49))-((8×3!)×9²÷3)+(sqrt(16)×(5!-4!)) math symbols do
3:15 btw triangle can be seen as the letter Delta from the greek alphabet, and the other one is Theta. (also from the greek alphabet) Delta is also usually used as the change of something. and theta im pretty sure equals rotation of a circle/circumference or just rotation, i dont know anything else
sigma is a mathematic symbol, not a meme?.
I pray every day that this is a joke lmao
@@roughcut001 back then sigma was a mathematic symbol
now: meme wtf
I know I didn’t learn more math from an 8 minute long video than years of school with atleast 2 hours spent in math each day
00:47 My stupid ass thought the square root was a tick.
It does look like one here.
@@TheCaregiverSITMOB In the days of yore, it was used in place of a tick on ScanDisk.
I lost track of those symbols the moment we got past the equal sign and approximately sign
6:37 You mean "lemniscat symbol"
Oh shut up
Lemni-SCAT symbol anyways
Thanks for the video, it helped me learn calculus 👍👍
6:42 the infinity starts
My head hurt. I should be in summer vacation... 💀
6:30 Sigma🗿🍷
Lol
sigma in math ✅
sigma in brainrot 💀
Thanks for this video. It's really helpful for me.
OG's will remember back when sigma was an actual math symbol
Yes, I do remember the present.
Bro literally teached us how to do math in the correct way
Mathematicians calling them imaginary numbers instead of admitting they were wrong...