Just a quick error on your side regarding “e” : the number wasn’t actually named after Euler, it just so happened that he was working on several different numbers at that time and named them “a”, “b”, and so on. The fact that the only number that ended up mattering was named “e” is purely coincidental.
@@isavenewspapers8890 Nah, Euler just asked a random name generator to come up with a good name for this number and it popped out "Euler" by sheer coincidence.
Aleph null ^ Aleph null is not equal to Aleph null. Aleph null ^ n = Aleph null where n is finite, but putting Aleph null as an exponent results in a larger infinity. Even 2 ^ Aleph null > Aleph null.
Yeah I was thinking the same thing. a^x is O(x^∞). Or, more precisely, lim h→0 (1+hx)^(1/h), making it O(x^(1/h)) in the limiting case as h→0, or O(x^w) in the limiting case as w→∞. If it was closed under even the most rapidly increasing elementary functions, there'd be no practical way to generate aleph 1.
@@kvOdratui you can quite easily prove that 2 ^ Aleph null > Aleph null, since you can find a bijection between a set of size 2 ^ Aleph null and a set of the cardinality of the real numbers
@@kvOdratuiNo, it is definitely known that 2^Aleph0 > Aleph0 (by Cantor's theorem). What we do not know (and in a certain sense cannot know) is whether 2^Aleph0 = Aleph1 (continuum hypothesis).
6:50 Yeah I did a double take when I heard that line too! I was like “WTF dude? 3 is not a variable! It’s a fixed value, and that value is fixed at 3.”
Thanks for this informative video. Unfortunately, you give the impression that the Ancient Greeks chose the name π for π when in actual fact it was the Welsh mathematician William Jones in 1706, so its use is actually relatively recent.
Yup! It's because every non-integer rational is also not an integer when squared. This is because when a rational is not an integer, that means the denominator has something in its prime factorization that the numerator doesn't, and this doesn't change when squaring, as squaring just adds another copy to the prime factorization of both the numerator and denominator
@andrewsaur2729 Thanks for that really clean explanation. I had a little bit of an intuition for that fact that squaring decimal numbers doesn't create integers yesterday. But I'm still astounded by that fact. It seems like something that should have come up in a math class at some point. Like I always thought it was crazy that the square root of two is irrational and right under my nose are all these other irrational square roots.
It feels like 0 is placed strangely late into the video. I'd have thought it'd be one of the first constants you mentioned. Also, I can't believe the number 1 didn't get a section. By the way, I wish you'd have given τ (tau) a mention. I mean, Tau Day was only a few days ago, after all. (For those of you who don't know, the number τ is defined as the ratio of a circle's circumference to its radius, equal to 2π and approximately 6.28. The use of τ clarifies radian angle measurements; for example, 1/4 turn = τ/4 rad, 1/6 turn = τ/6 rad, and so on.)
I Love all the constants in Math because i am an Theoretical MATHEMATICIAN. But my most favorite or i could say the most DANGEROUS ones are 0 (Holy) and the ALEHP NULL (sorry hell) !!!!!! Because I am the type of Expert MATHEMATICAIN who don’t really understand MATH and the REALITY (or PHYSICS) R u there with me???
Pi wasn't "discovered" by one guy, Archimedes calculated its value to an impressive degree but that just represents one in a series of refinements on the known value. It was known for centuries before Archimedes by various civilizations that pi is a bit more than 3, since that isn't hard to deduce. It's harder to deduce more precise values, but I wouldn't call that "discovering pi".
@@nzqarc technically, we cannot say whether 2^aleph zero = aleph zero, because that is the continuum hypothesis which is undecidable (neither true nor false) in ZFC
@@nzqarc we do know, it's whatever we choose it to be. Both options, where it does equal aleph 1 and where it doesn't equal aleph 1, can be consistent, so both can be correct and we can choose the one we want. Like the statement "x³=1 has exactly one solution". We can let it be true, or false, and both work, but we have to live with the consequences. The consequences of making it true is that we must not have complex numbers, and making it false means we must have complex numbers.
It is a constant because it is a specific number with a specific (albeit imaginary) value. 3i, 4i, etc are also their own numbers. It is just like the imaginary version of "1". Sometimes it is called the imaginary unit, which is maybe more in line with what you are thinking. But it is not a variable.
My favorite branch of mathematics is probably complex analysis or fractional calculus. :3 But I don't know how much I know about them, I just like them.
My favorite branch of Mathematics is abstract Algebra and my favorite constants are both e and pi because they share something mysterious which we don't really understand yet. I mean Eulers Identity is not a coincidence.
Right, guys. Quick question: if something is irrational, it has infinite digits. Yes? If it has infinite digits, then all of the possible arrangements of those digits will appear, yes? We know that 314 can appear in pi many times, and 314159265358979323 can also appear in pi, yes? So then if there’s infinite arrangements of these digits, then all of them will appear in an irrational number, yes? So then if they all appear, wouldn’t one possibility be that that number repeats over and over again? So therefore, if you go far enough into an irrational number, then you will find that it repeats and as a result isn’t irrational, yes? Idk if I’m right or not, but I was just thinking about it
no well first of all it's unknown whether pi is normal (for all we know it could devolve into 010010001000000100000000001 or whatever) secondly no because 0% probabilistic chance
It isn't named BY Euler? No, he certainly did name the number "e". If you mean it isn't named AFTER Euler, that's also wrong, since we commonly call it "Euler's number".
The golden ratio is not just *an* irrational number. It is the *most* irrational number, in that it is farthest from any rational number that an irrational number can be.
It isn't really a famous constant, it is just an interesting possible solution to certain infinite series. But it's not like it had to be "discovered" as with most of the constants here.
It needs to be a ratio of integers, for any given circle if the diameter is an integer, the circumference will be irrational, and vice versa, so their ratio will never be a rational number
@@ThoughtThrill365 I mean ig you can take it as a comp or a joke over some names you said being pronounced pretty uh let's just say............little uh bad.
i is distinguished from -i in complex numbers very clearly, isn't it? 3+4i and 3-4i aren't the same. Even if you just look at the imaginary number line, like on an Argand plane, obviously -i is just the negative of i, exactly like with real numbers. i-i is also 0, for example.
@@HuckleberryHim you misunderstand. Consider the set {i,-i} and select a random ι in that set. Then write some expressions that use i, but replace each i with ι. You won't be able to tell which one you chose. They're functionally identical. sin(z)=(e^(ιz)-e^(-ιz))/(2ι) e^(πι)=-1 ι²=-1 e^(πι/2)=ι ι+(-ι)=0 ι(-ι)=1 lim(z→∞) sec(ι|z|)=0 sin(ιz)=ιsinh(z) Et cetera, et cetera. If you called -i=j and redrew the argand diagram with this in mind, nothing would change. The only reason we know i and -i are not the same is that they add to 0, but are not themselves 0 because they multiply to 1. This is why there's no ordering in the complex plane. i>0 is false, as is i
The dimensionless constants in physics aren't always so relatively nicely close to small integers. The fine structure constant is approximately 1/137, while the difference between the predicted vacuum energy and the observed vacuum energy is roughly 10^120. Planck units might be 0 or 1 naturally, but in our system of measurements, their magnitudes can be even more wild. Still, you're right that a lot of numbers in math and science are either integers close to 0 or relatively simple fractions (like 5/3 for turbulence). Is this because we build so much of our math off the simple numbers, so they always keep coming along for the ride? Or is there something fundamental about integers and rationals that's "intrinsic" to logic and the Universe themselves?
I do coding, but we have something called fast fourier transform which is used in acoustics which i guess kinda relates to electrical engineering?? @lakshya4876
Just a quick error on your side regarding “e” : the number wasn’t actually named after Euler, it just so happened that he was working on several different numbers at that time and named them “a”, “b”, and so on. The fact that the only number that ended up mattering was named “e” is purely coincidental.
That's actually really cool
I heard he was only using vowels, and he used a already
While the name "e" did not come from Euler's name, the name "Euler's number" certainly did.
🤓🤓🤓🤓
@@isavenewspapers8890 Nah, Euler just asked a random name generator to come up with a good name for this number and it popped out "Euler" by sheer coincidence.
bro said Rayman instead of Riemann
not a big deal dude 🙃🙃
AI is not good at proper nouns. Also note the weird way is says "Pythagoras."
That's cause everyone loves Rayman
also Fibonaki? 😂
AI is reading it..
My favourite constant is 1
Fr?😅
@@Weskool1 It's a very special number and pops up everywhere in math, has a lot of interesting properties too
Ok but
π=3
e=3
π=e
e=2
2=√2
√2=1
sin(x)=x
cos(x)=1
∫f(x)dx=c
i≈1
nah bro 0 clears
What a chad.
The fact he pronounces Pythagoras in multiple ways and doesn't get it right in any way is humorous
Many of the names of things were a bit fishy.
Aleph null ^ Aleph null is not equal to Aleph null. Aleph null ^ n = Aleph null where n is finite, but putting Aleph null as an exponent results in a larger infinity. Even 2 ^ Aleph null > Aleph null.
Not quite. We *think* that this is true, but we don’t know, we can’t prove it.
Yeah I was thinking the same thing.
a^x is O(x^∞). Or, more precisely, lim h→0 (1+hx)^(1/h), making it O(x^(1/h)) in the limiting case as h→0, or O(x^w) in the limiting case as w→∞.
If it was closed under even the most rapidly increasing elementary functions, there'd be no practical way to generate aleph 1.
@@kvOdratui you can quite easily prove that 2 ^ Aleph null > Aleph null, since you can find a bijection between a set of size 2 ^ Aleph null and a set of the cardinality of the real numbers
@@kvOdratuiNo, it is definitely known that 2^Aleph0 > Aleph0 (by Cantor's theorem). What we do not know (and in a certain sense cannot know) is whether 2^Aleph0 = Aleph1 (continuum hypothesis).
there is too many Alehp Nulls to understand this
Aleph null to the power of aleph null is continuum. (10:43)
what
Wrong. Aleph_0 is the cardinality of the natural numbers. According to Cantor, the continuum is the power set of Aleph_0, or 2^(Aleph_0).
6:50 “The exact value of three is not known”
jokes on you, it’s 3
11:27 i see france
6:50 Yeah I did a double take when I heard that line too! I was like “WTF dude? 3 is not a variable! It’s a fixed value, and that value is fixed at 3.”
Please never pronounce Pythagoras that way again
Agreed
Ikr
Thanks for this informative video. Unfortunately, you give the impression that the Ancient Greeks chose the name π for π when in actual fact it was the Welsh mathematician William Jones in 1706, so its use is actually relatively recent.
Hmmmm, I thought it was named π because the first letter of the word describing it is π.
1:50 Most insane pronunciation of Pythagoras I've ever heard.
Don’t forget he said “pie-the-gore-ass” 💀
White theme: can't watch at night
Dark theme: can watch anytime
3:40 holy cow trumps ear! wot wot this was released a month ago! whoaa
This video was actually cool, I learnt a lot, you’re videos in general are interesting
Nice video as always 😏 Maybe can you make film about types of numbers like natural, surreal, p-adic? 😎
Thanks for the idea!
LMAO that trump ear i was so supprised for a second 😂😂😂
I didn't know that the square root of every non perfect square is irrational. That's absolutely wild.
Yup! It's because every non-integer rational is also not an integer when squared.
This is because when a rational is not an integer, that means the denominator has something in its prime factorization that the numerator doesn't, and this doesn't change when squaring, as squaring just adds another copy to the prime factorization of both the numerator and denominator
💀
Same
@@andrewsauer2729Wow that’s actually really cool! How have I never heard of this
@andrewsaur2729
Thanks for that really clean explanation. I had a little bit of an intuition for that fact that squaring decimal numbers doesn't create integers yesterday. But I'm still astounded by that fact.
It seems like something that should have come up in a math class at some point. Like I always thought it was crazy that the square root of two is irrational and right under my nose are all these other irrational square roots.
4:56 change your smoke detector bro
it sounds too stretched out to be a smoke detector
i want to but its hard to reach and im kinda lazy 🦥 😂
LOL i didn’t notice that
NOT 10 SECONDS IN AND I HEAR A CEILING BIRD. THE SMOKE DETECTOR IS CRYING IN ANGUISH.
It feels like 0 is placed strangely late into the video. I'd have thought it'd be one of the first constants you mentioned. Also, I can't believe the number 1 didn't get a section.
By the way, I wish you'd have given τ (tau) a mention. I mean, Tau Day was only a few days ago, after all. (For those of you who don't know, the number τ is defined as the ratio of a circle's circumference to its radius, equal to 2π and approximately 6.28. The use of τ clarifies radian angle measurements; for example, 1/4 turn = τ/4 rad, 1/6 turn = τ/6 rad, and so on.)
Can you collaborate with me to make videos better? If interested, send me an email 📨
@@ThoughtThrill365 Is there money involved?
yes, pls send me an email, we will discuss.
@@ThoughtThrill365 What's your email address?
@@ThoughtThrill365Okay, what's your "mailbox", if you know what I'm saying?
(TH-cam is being ridiculous right now.)
It’s like this guy actively tried to mispronounce as many names as possible.
it's the opposite, i actively tried to correctly pronounce.
Bro make 80% is greek letter💀💀💀💀
I Love all the constants
in Math because i am an Theoretical
MATHEMATICIAN. But my most favorite or i could say the most DANGEROUS ones are
0 (Holy) and the ALEHP NULL (sorry hell) !!!!!!
Because I am the type of Expert MATHEMATICAIN who don’t really understand
MATH and the
REALITY (or PHYSICS)
R u there with me???
did you drank cocaine?
"adolf kinkelin"
theres 2 things that could go horribly wrong
Every physics constant? Or would that take too long
Every? Impossible. The most notable ones , yes , but it would still take a long time.
If you're looking for a change of pace , how about every medical/surgical specialty explained
Pi wasn't "discovered" by one guy, Archimedes calculated its value to an impressive degree but that just represents one in a series of refinements on the known value. It was known for centuries before Archimedes by various civilizations that pi is a bit more than 3, since that isn't hard to deduce. It's harder to deduce more precise values, but I wouldn't call that "discovering pi".
isn't aleph null ^ aleph null = aleph one?
We don't know, maybe.
n^aleph 0 ≥ aleph 1
@@nzqarc technically, we cannot say whether 2^aleph zero = aleph zero, because that is the continuum hypothesis which is undecidable (neither true nor false) in ZFC
That is what I remember. I believe the book was Asimov on Numbers from a long time ago. But maybe we learned more in the last 40+ years!
@@nzqarc we do know, it's whatever we choose it to be. Both options, where it does equal aleph 1 and where it doesn't equal aleph 1, can be consistent, so both can be correct and we can choose the one we want.
Like the statement "x³=1 has exactly one solution". We can let it be true, or false, and both work, but we have to live with the consequences. The consequences of making it true is that we must not have complex numbers, and making it false means we must have complex numbers.
Is “i” actually a constant? I always viewed it as an imaginary variable. I very well could be wrong though.
It is a constant because it is a specific number with a specific (albeit imaginary) value. 3i, 4i, etc are also their own numbers. It is just like the imaginary version of "1". Sometimes it is called the imaginary unit, which is maybe more in line with what you are thinking. But it is not a variable.
Can an irrational number be expressed as a ratio of two integers?
No, the definition of irrational numbers is the exact opposite of that.
1:23 Show me an example of a real number that is neither rational nor irrational!
Useless.
My favorite branch of mathematics is probably complex analysis or fractional calculus. :3
But I don't know how much I know about them, I just like them.
א null?
A ton of mispronunciations, including the name of the great Bernhard Riemann.
My favorite branch of Mathematics is abstract Algebra and my favorite constants are both e and pi because they share something mysterious which we don't really understand yet. I mean Eulers Identity is not a coincidence.
10:43 is incorrect tho
It is literally equal to 2^aleph(0)
The first thing you 🎉should always be a good thing to have a positive good 😊 day ahead your 🎉😢vintwz
I think you forgot a few of the constants, such as 1, 2, 3 and there are more I think
Eh, probably only a couple. I don't think he missed too much by leaving them out.
@@General12th wait but omg he also forgot 0, -1, -2, and maybe a few more in that direction
i like your videos the pronunciation is funny though
8:51💀
Right, guys. Quick question: if something is irrational, it has infinite digits. Yes? If it has infinite digits, then all of the possible arrangements of those digits will appear, yes? We know that 314 can appear in pi many times, and 314159265358979323 can also appear in pi, yes? So then if there’s infinite arrangements of these digits, then all of them will appear in an irrational number, yes? So then if they all appear, wouldn’t one possibility be that that number repeats over and over again? So therefore, if you go far enough into an irrational number, then you will find that it repeats and as a result isn’t irrational, yes? Idk if I’m right or not, but I was just thinking about it
no
well first of all it's unknown whether pi is normal (for all we know it could devolve into 010010001000000100000000001 or whatever)
secondly no because 0% probabilistic chance
Watching this video for no reason and understanding nothing (only i understand is pi)
√2 is also algebraic which is nice. π for example isn't
bro the catalan thing graph looks like a bunch of frances
Are you trying to mispronounce every word? lmao
φ is also the diagonal of a pentagon with side 1
1
0:08 bros got the beep
e isn't named by euler
True :3
It isn't named BY Euler? No, he certainly did name the number "e".
If you mean it isn't named AFTER Euler, that's also wrong, since we commonly call it "Euler's number".
@@isavenewspapers8890 Well I think what he meant is that it wasn't called "e" in honor of Euler. Obviously. And that is true.
unrelated to the vid by why tf did i sit down to watch a nice math video to then get slapped in the face by A 6:40 UNSKIPPABLE ADD ON EVE ONLINE WTF
What is 1+i times sq root of 3
you forgot 4
Eulers number is e to the power of i times pi
Eulers number is just e
thanks
It's Hermann Kinkelin, not Adolf Kinkelin.
12:10 Definitely calculus
Weird to call it Pythagoras’ number when he was the one claiming it wasn’t irrational 😭😭😭😭
א
10:59 Maybe, aleph-zero is not closed under expotenciation, after all?
My favourite is e and the chaos numbers. Although it’s said to see no talk on the monster number from group thoery
Transcendental
Is it just me or did bro sometimes change his pronunciations? Bifurcation is an example…
Bro I can’t get over how many times he mispronounced names and letters 😭😭
11:51 Don't you mispronounce Ramanujan's name! I admire that mathematician!
Who cares if he spelled some of those names wrongly, great vid sir.
PI was known thousands of years earlier before Archimedes and the Greek please mention that, you do not get to make your history
π I
π
The constant mispronunciations are distracting.
tau > pi is true in all ways
perimetros means perimeter, not circunference
The perimeter of a circle is its circumference.
These are exactly the same
Rayman
The golden ratio is not just *an* irrational number. It is the *most* irrational number, in that it is farthest from any rational number that an irrational number can be.
this is kinda bogus unless you rigorously define "closeness"
my favourite constant is g = pi^2 = e^2 = 9
I love probabilities
This is definitely gonna help me with my studying!
Everywhere I look I see Dan ~ Reform ~ .
8:10 why did you draw the 1
What about-1/12?
It's a number, for sure.
@@isavenewspapers8890 I agree
It isn't really a famous constant, it is just an interesting possible solution to certain infinite series. But it's not like it had to be "discovered" as with most of the constants here.
the question that bothers me is why is pi an irrational number if it is defined as a ratio. Rational numbers are can be defined as ratios.
It is a ratio of two quantities, but one of those quantities is not an integer. To be rational it would need to be a ratio of two integers
It needs to be a ratio of integers, for any given circle if the diameter is an integer, the circumference will be irrational, and vice versa, so their ratio will never be a rational number
Every number x can be written as a ratio, like x/1. But rational means we can do it with integers specifically.
Do you do physics too?
Yes sir
Get this man to 10k subs!
Is that “The Donny” in the golden ratio clip 😂🤯
0:13 means perimeter literally
Where is Euler's number e?
i ≠ √(-1) because the square root function is not defined over the negative number.
However, i² = -1, but also (-i)² = -1.
It is defined, but it's not single valued.
If 0 = 0 + 0i then 0D = 0D + 0Di.
Aleph NO?
Or is that Aleph-zero or Aleph-nought?
“Aleph Null”
Unsigned infinity?
incredible, well done!
Trigonometry is my jam
Which text to speech AI do you use? It's pretty good apart from minor pronunciation errors.
bro, it's not ai voice.
@@ThoughtThrill365lol
@@ThoughtThrill365 I mean ig you can take it as a comp or a joke over some names you said being pronounced pretty uh let's just say............little uh bad.
@funwithtommyandmore i agree with you xD
@@ThoughtThrill365 :)
0:00 Pi=314
I like algebra
i is not *the* square root of -1. It is *a* number that satisfies i^2 = -1. Technically, i can't be distinguished from -i.
Bruh what
And Mathematics and Physicists chose the opposite values, so j=-i. (this is a joke)
i is distinguished from -i in complex numbers very clearly, isn't it? 3+4i and 3-4i aren't the same. Even if you just look at the imaginary number line, like on an Argand plane, obviously -i is just the negative of i, exactly like with real numbers. i-i is also 0, for example.
@@HuckleberryHim you misunderstand. Consider the set {i,-i} and select a random ι in that set. Then write some expressions that use i, but replace each i with ι. You won't be able to tell which one you chose. They're functionally identical.
sin(z)=(e^(ιz)-e^(-ιz))/(2ι)
e^(πι)=-1
ι²=-1
e^(πι/2)=ι
ι+(-ι)=0
ι(-ι)=1
lim(z→∞) sec(ι|z|)=0
sin(ιz)=ιsinh(z)
Et cetera, et cetera.
If you called -i=j and redrew the argand diagram with this in mind, nothing would change. The only reason we know i and -i are not the same is that they add to 0, but are not themselves 0 because they multiply to 1.
This is why there's no ordering in the complex plane. i>0 is false, as is i
why are universal constants so small?
The dimensionless constants in physics aren't always so relatively nicely close to small integers. The fine structure constant is approximately 1/137, while the difference between the predicted vacuum energy and the observed vacuum energy is roughly 10^120. Planck units might be 0 or 1 naturally, but in our system of measurements, their magnitudes can be even more wild.
Still, you're right that a lot of numbers in math and science are either integers close to 0 or relatively simple fractions (like 5/3 for turbulence). Is this because we build so much of our math off the simple numbers, so they always keep coming along for the ride? Or is there something fundamental about integers and rationals that's "intrinsic" to logic and the Universe themselves?
Electrical engineers do *not* use i! (We call it j, because i is already used for electrical current.)
i factorial?!?
That means you use the number i, and you use the symbol i; you just don't use the latter for the former.
Why do you need imaginary numbers in electrical engineering?
I do coding, but we have something called fast fourier transform which is used in acoustics which i guess kinda relates to electrical engineering?? @lakshya4876
Quantem
π = C/d
fucking rayman bruh
Yeah pronunciation is not…. His strong suit….