I am a chemist, I calculate, then I realize I am too lazy, so I just approximate. Then I do the experiment and see that the appeoximation does not work in reality.
Watching this video is way better than going on reddit and scrolling. It's way easier to listen to what Flammable Maths says than opening a new tab and searching stuff every time you don't understand something.
29:30 So these guys are suggesting that math is racist based on statistics. Statistics is a field of mathematics, therefore they used racist and unethical means to reach this conclusion
for the rearranging it has to be conditionally convergent. divergent series taking those values happen because they are misapplying properties (like the existence of an additive inverse), not because they go to those values.
28:10 If 1 and 2 are considered under their usual definition (1={ø} and 2={ø,{ø}} where ø is the empty set), then it is manifest that the set {1,2} contains two distinct elements, while {1} contains just one element, disallowing any surjections from {1} to {1,2}; this is no problem under constructivism. I believe the OP confused this with the statement-or a similar statement-that under constructivism, it is not provable that the set {a,b} is finite-let alone countable-for any two arbitrary sets a,b. This is because the proposition entails by a routine calculation that any pair of sets are either equal or not equal, which can be shown to be logically equivalent to the excluded middle
@@PapaFlammy69 should have said to your 7th grade class that "math is arbitrary and typically things are defined in a certain way because they are useful when defined that way. You could just as easily define it another way, but it might not work out logically with other parts of math, or simply be useless"
7:05 - Those are the fundamental operators. Addition, multiplication, exponentiation, tetration, pentation, hexation, etc. And in the case of 2{operator}2 it's always equal to 4. 27:25 - The graph is doing what drunk people do. Start doing something that they won't complete because they'll feel tired before they can even get going, they get hungry out of nowhere and they find others more attractive than usually.
"Poisson" means fish in French. And that meme was referring to a famous story from the New Testaments (when Jesus satiated hungry people with bread and fish by Ctrl+C/Ctrl+V
Believe it or not, fractional derivatives actually have a huge number of applications. One is dispersion of waves and I have also worked with fractional calculus in a cosmology context. I am saying that just by curiosity and fun, I enjoyied the video and I like you channel
7:23 is a good meme. I think their notation is wrong though, it should be 2[n]2 not 2{n}2 But Bassically 2+2 = 2[1]2 2 × 2 = 2[2]2 2^2 = 2[3]2 It's a generalized notation for repeating the previous operation. For 2 though it's the same for any n.
They're just operations and hyperoperations. In order, going anticlockwise: addition, multiplication, exponentiation, tetration, pentation, hexation. Afaik, exponentiation is noted as x[1]y, tetration as x[2]y, and so on though 🤔.
5:20 I know 4 meanings of x=x+1 in normal programming languages: - In Pacsal, this is a comparison. It is always false for integer types of x, but it is true for large enough real x's - In many languages, including Python, this is an assignment. It can be thought of as “x after this = x before this + 1”. However, it usually can be also written as “x += 1” and, in some languages, “++x” - In Python, if passed to a function, it is a keyword argument. If the function has an argument called x, it means “x inside the function = x in the scope where it is called from + 1” - Also in Python, if specified as an argument for a function when defining it, it is a default argument, meaning “x in this function if not given = x in the scope where it is defined + 1”. The addition is done when defining the function
23:44 While this reasoning takes out Brinner, Dinfast is still valid because two given meals of a day can be different but congruent (modulo one day). There can be a meal *after* dinner, *before* breakfast. (which would typically be eaten around 2~3AM)
7:11 That notation is the beginning of BEAF used in googology. The way it works is: a*b = a+a+..+a with b 'a's a^b = a*a*..*a with b 'a's a{4}b = a^a^..^a with b 'a's a{5}b = a{4}a{4}..{4}a with b 'a's in general a{b+1}c = a{b}a{b}..{b}a with c 'a's It is just another way of representing hyperoperators/knuth's up arrows (but the BEAF notation goes further beyond just hyperoperators).
Well yes but I think it's still very abstract for 7th graders and would be hard to understand. Although probably one of the easiest. I learned that by using a infinite busses with infinite seats, which i thought worked well.
Not sure if someone commented this already, but the series in 3:50 converges and all the operations make sense in the field of 2-adic numbers, so the end result should also be valid, and indeed S = -1 in 2-adics. This also explains why your factoring out 4 leads to the same (correct) result.
@@liweicai2796 Does that agree with the epsilon-N definition of the sum of an infinite series though? Methinks not. There's that caveat that people tend to forget.
@@Kurushimi1729 Yeah, that's true. if the series over (an) doesn't converge, then |(an)| doesn't either. But if (an) converged, |(an)| would need to converge, so that every rearrangement had the same limit. Absolute convergence was just the term he was looking for.
The value of -1 does make sense in some contexts, like the continuation of y = 1/(1-x). It's not a completely invalid result, it just depends on what you mean.
29:32 It's not that your skincolour defines your intellect, but rather that the skincolour of your parents defines their wealth, which in turn influences your "school smarts".
6:00 you can right it as "x += 1" instead so you can sort of trick your mind into thinking you're assigning the variable x rather than going against all math
Probably not so crucial for your content, but I think I heard a famous paradox that helps explain the cardinality of N, Z and Q, it has something to do with an hotel with infinite rooms. Maybe you could use it to help your students understand. Anyway love your content Papa Flammy, keep it up!😁
@@rubixtheslime I agree. Or they could've just used 4 guys for 2+2, 2*2, 2(n arrows)2 (for all n>=1), and ellipses. That way it wouldn't stop at hexation.
Here‘s a joke I came up with: „Infinitely many men go into a bar. The first orders 1 beer, the second 2 beer, the third 3 beer, and so on. After a couple more men ordered the bar keeper says:
At 3:56 I think you are referring to Riemann's Theorem for simply convergent (convergent but not absolutely convergent) series. To get that result you need the general term of the series to go to 0 tho. In that way you are able to rearrange the terms of the series to get whatever number you want. So that series would not work even if you were to consider Sum_{n in N} (-1)^n 2^n.o
12:32 also if you accept the premise that points means corners in this context, there are many shapes that have corners and still roll - object of constant width, they're called.
Besides enjoying the memes of that FB group, I remembered something very saddening. I used to post memes regularly in that group and one day someone blocked me from the group. :(
That S = −1 is actually how signed integers are sorted in computer programs, except the number of bits are obviously finite. If you’re using 8 bits, −1 is equal to 1+2+4+8+16+32+64+128 (all 8 bits on).
I’m trying to find out where I get the audacity to keep showing up to these videos knowing me and my engineering team almost failed our thermo final because we couldn’t solve the basic algebra problems after doing all the complicated integrals and inequalities 😭🙈😭😮💨
4:45 Tbf I'm just an adolescent with no natural understanding nor education of calculus, however I understand that the last expression is legendary thanks to it defining a theorem complex like the previous diagram however contracting it to something more legible than posh eye strain
3:33 for this one, it actually doesn’t matter where you start factoring, that method will always be -1. As a quick sketch, you start with S=1+2+4+8+…, then wherever you start factoring, the terms before will be a sum of n-1 powers of two which is trivially 2^n-1 (the proof of which is left as an exercise to the reader) then you factor out a 2^n from the remaining terms. Using these, they yield S=2^n-1+S*2^n. This can be rearranged, to S(2^n-1)=-(2^n-1), which reduces to S=-1 for any factor point. Alternatively, one of 3blue1brown’s oldest videos actually covers this sum: th-cam.com/video/XFDM1ip5HdU/w-d-xo.html
@17:06 not sure how deep this is, the quote comes from Arrowverse/Flash crossover episode and the pun with Banach-Tarski, which refering to sortof volume of a sum of pointmasses and the quote "every cell of my body", trying to imagine this for real. Feels deep. 🤔
02:49 following this logic you also cant have a disk in real life because there are also dimensions in which a disk got no expansion. In reallife we can only cut out a cylinder (at least approximatly). 03:46 When a series is not absolutely convergent but convergent you can get every real number as a limit by rearranging the summands. But i feel like for this sum there should be some other values we can reach by doing simmilar stuff. 22:52 I had to like there
One question, I got something that looks close but not exact to cos, instead I got some function with some part of it definitely being cos, but its absolute value asymptomatically grows as it gets closer to 0
@4:35 the 🤔 is the variable. I like this task. One could solve integral first with the 3 constants and then search for their value as linear equation system. While technically only solve integral_a'^oo sin(x)/x dx is sufficient - not sure yet, why it's a meme, probably due to pictograms instead letters
The meme with the rider with cool jacket and white bullet is so me. I often try to find a formula so the result of all the numbers on the registration plate will be zero for no reason. Is this just me?
32:16 I don't get the meme. 1 isn't prime because a prime is defined as a composite number that can only be divided by itself and 1. A composite number is a number with more than 1 factor, therefore 1 isn't a prime because it only has 1 factor (itself).
![You Laugh, You Math... [ feat.@AndrewDotsonvideos ]](http://i.ytimg.com/vi/ZpBWdzS-I7g/mqdefault.jpg)
"Why be right when you can approximate" - engineers
Ah, I see you are pandering to your ever increasing physicist audience
:D
I am a chemist, I calculate, then I realize I am too lazy, so I just approximate. Then I do the experiment and see that the appeoximation does not work in reality.
@@isi2973
approximations: created to allow easier calculations in reality
also approximations: fail to work in reality
But engineers aren't wrong ; they just didn't run infinite steps in approximation to become right.
I'm sure that he has more tan 2 physicist watching xD
Watching this video is way better than going on reddit and scrolling. It's way easier to listen to what Flammable Maths says than opening a new tab and searching stuff every time you don't understand something.
:D
29:30 So these guys are suggesting that math is racist based on statistics. Statistics is a field of mathematics, therefore they used racist and unethical means to reach this conclusion
4:45 might want to be careful shortening complex analysis like this..! i was dying laughing each time i heard it lmao
:D
He was very careful, it was very intentional.
6:30 I'm feeling recursive, and so am I.
11:44 I started dying of laughter when he called taylor swift "some woman"
for the rearranging it has to be conditionally convergent. divergent series taking those values happen because they are misapplying properties (like the existence of an additive inverse), not because they go to those values.
28:10
If 1 and 2 are considered under their usual definition (1={ø} and 2={ø,{ø}} where ø is the empty set), then it is manifest that the set {1,2} contains two distinct elements, while {1} contains just one element, disallowing any surjections from {1} to {1,2}; this is no problem under constructivism. I believe the OP confused this with the statement-or a similar statement-that under constructivism, it is not provable that the set {a,b} is finite-let alone countable-for any two arbitrary sets a,b. This is because the proposition entails by a routine calculation that any pair of sets are either equal or not equal, which can be shown to be logically equivalent to the excluded middle
19:49 You are already transforming into those boomer professors lmfao
xDDD
@@PapaFlammy69 should have said to your 7th grade class that "math is arbitrary and typically things are defined in a certain way because they are useful when defined that way. You could just as easily define it another way, but it might not work out logically with other parts of math, or simply be useless"
7:05 - Those are the fundamental operators. Addition, multiplication, exponentiation, tetration, pentation, hexation, etc. And in the case of 2{operator}2 it's always equal to 4.
27:25 - The graph is doing what drunk people do. Start doing something that they won't complete because they'll feel tired before they can even get going, they get hungry out of nowhere and they find others more attractive than usually.
Ngl I cracked when you pulled the ,,er wusste nicht was er tat“ rant - reminds me that I have to take my german final soon :)
:D
"Poisson" means fish in French. And that meme was referring to a famous story from the New Testaments (when Jesus satiated hungry people with bread and fish by Ctrl+C/Ctrl+V
ohhhhhhhhhhhhhhhh xD
And there was me thinking it was to do with the misapplication of Poisson distributions…
@@KusacUK Why not both?
Believe it or not, fractional derivatives actually have a huge number of applications. One is dispersion of waves and I have also worked with fractional calculus in a cosmology context. I am saying that just by curiosity and fun, I enjoyied the video and I like you channel
7:23 is a good meme.
I think their notation is wrong though, it should be
2[n]2 not 2{n}2
But Bassically 2+2 = 2[1]2
2 × 2 = 2[2]2
2^2 = 2[3]2
It's a generalized notation for repeating the previous operation. For 2 though it's the same for any n.
2 is mind blowing
Unless you use BEAF, which chooses {}.
They're just operations and hyperoperations. In order, going anticlockwise: addition, multiplication, exponentiation, tetration, pentation, hexation. Afaik, exponentiation is noted as x[1]y, tetration as x[2]y, and so on though 🤔.
5:20 I know 4 meanings of x=x+1 in normal programming languages:
- In Pacsal, this is a comparison. It is always false for integer types of x, but it is true for large enough real x's
- In many languages, including Python, this is an assignment. It can be thought of as “x after this = x before this + 1”. However, it usually can be also written as “x += 1” and, in some languages, “++x”
- In Python, if passed to a function, it is a keyword argument. If the function has an argument called x, it means “x inside the function = x in the scope where it is called from + 1”
- Also in Python, if specified as an argument for a function when defining it, it is a default argument, meaning “x in this function if not given = x in the scope where it is defined + 1”. The addition is done when defining the function
23:44
While this reasoning takes out Brinner, Dinfast is still valid because two given meals of a day can be different but congruent (modulo one day). There can be a meal *after* dinner, *before* breakfast.
(which would typically be eaten around 2~3AM)
Also, if someone, potentially a hungover student, oversleeps and wakes up at dinnertime, that would be their breakfast i.e. brinner.
7:11 That notation is the beginning of BEAF used in googology.
The way it works is:
a*b = a+a+..+a with b 'a's
a^b = a*a*..*a with b 'a's
a{4}b = a^a^..^a with b 'a's
a{5}b = a{4}a{4}..{4}a with b 'a's
in general
a{b+1}c = a{b}a{b}..{b}a with c 'a's
It is just another way of representing hyperoperators/knuth's up arrows (but the BEAF notation goes further beyond just hyperoperators).
You could have used the Hilbert Hotel to explain how some infinities are the same size as other infinities to your 7th graders.
Ted Ed video lol
Well yes but I think it's still very abstract for 7th graders and would be hard to understand. Although probably one of the easiest. I learned that by using a infinite busses with infinite seats, which i thought worked well.
Not sure if someone commented this already, but the series in 3:50 converges and all the operations make sense in the field of 2-adic numbers, so the end result should also be valid, and indeed S = -1 in 2-adics. This also explains why your factoring out 4 leads to the same (correct) result.
Or simply apply the same logic for 1+2+3+...=-1/12. 1/(1-z) is the analytic continuation of 1+z+z^2+... over C and it indeed equals to -1 when z=2.
also, the result he was referring to is for conditionally convergent series
Yep.
And if your topology arises from an absolute value on Q, this serie is either divergent or converges to -1.
@@liweicai2796 Does that agree with the epsilon-N definition of the sum of an infinite series though? Methinks not. There's that caveat that people tend to forget.
20:01 That caught me off guard
3:50 yes, the series is not absolutely convergent, therefore not every rearrangement of the series converges to the same value
No arrangement of this series converges at all
@@Kurushimi1729 Yeah, that's true. if the series over (an) doesn't converge, then |(an)| doesn't either. But if (an) converged, |(an)| would need to converge, so that every rearrangement had the same limit. Absolute convergence was just the term he was looking for.
The value of -1 does make sense in some contexts, like the continuation of y = 1/(1-x). It's not a completely invalid result, it just depends on what you mean.
@@Gretchaninov it has an even deeper meaning if one would apply exponential regularization or something like that.
it has to be conditionally convergent
29:32 It's not that your skincolour defines your intellect, but rather that the skincolour of your parents defines their wealth, which in turn influences your "school smarts".
What?
6:00 you can right it as "x += 1" instead so you can sort of trick your mind into thinking you're assigning the variable x rather than going against all math
When you're so angry you go german. That makes me chuckle
:D
I too tutor high school children and they make the mistake of dividing by “log” to solve: log(x) = 10
...
Press 25:58 for Flammable Maths getting so angry he reverts to speaking German
Probably not so crucial for your content, but I think I heard a famous paradox that helps explain the cardinality of N, Z and Q, it has something to do with an hotel with infinite rooms. Maybe you could use it to help your students understand. Anyway love your content Papa Flammy, keep it up!😁
Do you maybe mean Hilbert's hotel?
20:00 shit gave me mental whiplash I was not expecting that
27:27 People often make an analogy between random walks and being drunk eg. a drunk man in 2 dimensions or a drunk bird in 3 dimensions.
7:15 Those are the hyperoperators (albeit a weird notation for them). They all equal 4.
I think if they used knuth up arrows it would've made more sense, also probably make it so that you don't naturally read ellipsis second
@@rubixtheslime I agree. Or they could've just used 4 guys for 2+2, 2*2, 2(n arrows)2 (for all n>=1), and ellipses. That way it wouldn't stop at hexation.
Here‘s a joke I came up with: „Infinitely many men go into a bar. The first orders 1 beer, the second 2 beer, the third 3 beer, and so on. After a couple more men ordered the bar keeper says:
I was facepalming right there with you at 26:08
I too have prayed for guidance.
Jens the cia keeps calling me are you in some kind of trouble pls response
we all ded cause of my 9/11 baking joke
I've risen from the realm of digraphs and abstract nonsense to notify you that integral symbols in category theory are for things called (co)ends
Well, if you want to be that careful, might as well just call it a cylinder.
My man seriously don't know Taylor Swift and Pam from the office? 🤣
20:00
Jens Freud knows whats up
fun fact: x=x+1 would also upset computer scientists, they use x++
27:40 🥺 I think you would like ontological maths, Papa Flammy 🥺
:D
At 3:56 I think you are referring to Riemann's Theorem for simply convergent (convergent but not absolutely convergent) series. To get that result you need the general term of the series to go to 0 tho. In that way you are able to rearrange the terms of the series to get whatever number you want. So that series would not work even if you were to consider Sum_{n in N} (-1)^n 2^n.o
Yes, exactly! :)
Thx for the refresher, Riccardo! :3
@@PapaFlammy69 You're welcome. Great video as usual :)
12:32 also if you accept the premise that points means corners in this context, there are many shapes that have corners and still roll - object of constant width, they're called.
“There’s always one meal in between breakfast and dinner”
Unless you’re in finals week and eating Cheetos at 3 am.
Math meme basically went from Undergrad students (toward graduation) to pre calc student that heard about shit.
Besides enjoying the memes of that FB group, I remembered something very saddening. I used to post memes regularly in that group and one day someone blocked me from the group. :(
that sucks :(((
That's a very sad story halal Newton, sorry to hear that
F
That S = −1 is actually how signed integers are sorted in computer programs, except the number of bits are obviously finite. If you’re using 8 bits, −1 is equal to 1+2+4+8+16+32+64+128 (all 8 bits on).
Need more math meme reviews...
we all do ;_;
Btw: Amazing video! I am amazed how much physics I can understand having studied chemistry...
I’m trying to find out where I get the audacity to keep showing up to these videos knowing me and my engineering team almost failed our thermo final because we couldn’t solve the basic algebra problems after doing all the complicated integrals and inequalities 😭🙈😭😮💨
r i p
flammy roasting pam from the office makes me sad inside lol
4:45 Tbf I'm just an adolescent with no natural understanding nor education of calculus, however I understand that the last expression is legendary thanks to it defining a theorem complex like the previous diagram however contracting it to something more legible than posh eye strain
3:33 for this one, it actually doesn’t matter where you start factoring, that method will always be -1. As a quick sketch, you start with S=1+2+4+8+…, then wherever you start factoring, the terms before will be a sum of n-1 powers of two which is trivially 2^n-1 (the proof of which is left as an exercise to the reader) then you factor out a 2^n from the remaining terms. Using these, they yield S=2^n-1+S*2^n. This can be rearranged, to S(2^n-1)=-(2^n-1), which reduces to S=-1 for any factor point. Alternatively, one of 3blue1brown’s oldest videos actually covers this sum: th-cam.com/video/XFDM1ip5HdU/w-d-xo.html
20:01
ALABAMA INTENSIFIES
I haven’t watched the vid but 35 mins of math memes seems amazing
i can confirm that the memes are some quality stuff
24:15 dinfast is eating food at 2:00 am
Who the hell defines 3 as {{ø}}? 3={ø,{ø},{ø,{ø}}} is clearly the superior construction!
The ablian stuff gets even worse when one of the two elements they check is the identity element
Or Zero :'D
“And you 7th graders couldn’t add fractions properly” , 7th grade me who used the 13 properties of congruences : *bruh*
@17:06 not sure how deep this is, the quote comes from Arrowverse/Flash crossover episode and the pun with Banach-Tarski, which refering to sortof volume of a sum of pointmasses and the quote "every cell of my body", trying to imagine this for real. Feels deep. 🤔
i hadnt thought meme reviews could actually be good
Much better than the traditional meme reviews that you do
02:49 following this logic you also cant have a disk in real life because there are also dimensions in which a disk got no expansion. In reallife we can only cut out a cylinder (at least approximatly).
03:46 When a series is not absolutely convergent but convergent you can get every real number as a limit by rearranging the summands.
But i feel like for this sum there should be some other values we can reach by doing simmilar stuff.
22:52 I had to like there
Would you call a cd disk a cd cylinder then?
Wow I will be waiting for more meme reviews
That meme at 32:45 you skipped, was actually good meme😂
Math Meme Review: First time
Physics Meme Review: First time?
Math Meme Review: First time?
Physics Meme Review: First Time
I think Lunfast is the meal between lunch and the FOLLOWING breakfast.
3:46 that only works for series that are convergent but not absolutely convergent. That one is neither
One question, I got something that looks close but not exact to cos, instead I got some function with some part of it definitely being cos, but its absolute value asymptomatically grows as it gets closer to 0
19:50 lol
16:45 The panda example is a good example.
yeye :p
33:27 i actually put a plus i in my integrals
14:05 I think that's normal in computer graphics, I remember OpenGL was like that
For complex z, 1^z =1 is hardly the whole story...
@4:35 the 🤔 is the variable. I like this task. One could solve integral first with the 3 constants and then search for their value as linear equation system. While technically only solve integral_a'^oo sin(x)/x dx is sufficient - not sure yet, why it's a meme, probably due to pictograms instead letters
I've often referred to "Taylor Swift" as "Taylor Series". Love the memes!
What's the r in the formula at 1:29?
4:00 but it also is -1 when you factor with 4, and every number💀
Hmmm Discord Server when, I guess it's a good idea 😅
10:40 That's Pam from the American version of The Office. I don't think her image is shopped.
Yeye, I know, but it still looks so out of proportion to me lol
As a maths student
The meme with the rider with cool jacket and white bullet is so me.
I often try to find a formula so the result of all the numbers on the registration plate will be zero for no reason.
Is this just me?
- Mom, can I have a circle?
- We have a circle at home.
*the circle at home*: 💿
the Weierstrass function , or as I like to call it, the stockmarket function.
Thats a big guitar pick right there
20:23 welcome to computing science !
You really fast became my favorite TH-camr
:D
I see papa flammy has seen enough division by zero jokes/memes 9:23
Did he just really just said “complex anal” 4:45? I can’t stop laughing.
Plot twist : the seventh graders are faking interest in infinity so he doesn't make them solve problems in class
14:06 i always encountered in mathematics Z direction like this, in other engineering subjects Z is always upwards.
32:16 I don't get the meme. 1 isn't prime because a prime is defined as a composite number that can only be divided by itself and 1. A composite number is a number with more than 1 factor, therefore 1 isn't a prime because it only has 1 factor (itself).
3:44
I thought that it had to be conditionally convergent. Think it was called the reimann series theorem... so I dont think it applies here.
Papa flammy should do a german sayings and swears review
3:50 Is this Ramanujan summation?
Came for math memes, stayed for the racism and billionaire worship.
26:26 that's just an alternive notation for tan^-1
Alas, I always knew that brunch wasn't linearly independent.
3:15 actually it can't be anything as this series is convergent in the 2-adics, converging to -1.
Oh yeah i remember the bruh substitution. Good times.
WOW
Papa is back with the memes
:=)
29:00 a system of inequalities