An e-nteresting video: e is Irrational, a Classic Proof

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Let us proof a fact about everyones most favourite transcendental boi =) We are going to exploit the Tail of the exponential function, just like Papa Fourier did back then. Enjoy! =D

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[MadSideburns]

Mathematicians are funny.
They always make absurd statements in order to prove themeselves wrong, and by doing that they prove themeselves right.
That's whitchery.

[jrmc]

Since e=3 and 3 can be expressed as 3/1 and 3/1 ε Q. Then e is rational. Get rekt

[completeandunabridged.]

A short proof:
If exp (1)=e
Then by consequence of the "Big if true" theorem we can say that since exp(1) and e are both small numbers, then logically the above statement cannot be true, because neither are big using the converse "Small if false" theorem. QED.

[Cubinator]

I would have shown that e is transcendental, because then I get the irationality of e as a corollary :)

[thesinglemathnerd]

You should do the integral from 0 to pi/4 of ln(tan(x))*tan(x). It takes a lot of work including three applications of L’Hopital’s rule, all on the same limit, about three or so substitutions, integration by parts, and the series for ln(1+x), but you get a really nice answer out the other side that may or may not have to do with pi^2/6 in some indirect way :)

[duncanw]

Most channels: like, comment, subscribe
Papa Flammy: perform a supertask constructing all rational numbers such that for any number expressed as the ratio of two integers, the denominator is a multiple of 2

[ianprado]

That flying Euler head made me laugh so hard

[badnews]

Dude, you’re so ducking dope. Kinda got thrown off by your accent at the beginning, but your awesome topics still got me hooked.
Seems like you super enjoy it, which makes the viewer enjoy it too. Thanks.

[completeandunabridged.]

Say some gangsta's dissin your fly girl, just give him one of these.




exp (1)

[pi]

The first time a "who would win?" got a 50/50 vote perfectly split down the middle. This is beauty. Also, fun fact from basic physics:

If PE or U=1 and KE=1+1/2+1/6+1/24+1/120+..., then E=e

[rkprimemaster]

These spicy bois never get old. Keep up man!

[APPLEZACKS]

The best part of my day is watching your videos.

Thanks papa flammy ❤️

[yoda-ghost]

Thanks for the video man :) e-asy to understand, and in my opinion the memes make it interesting and differentiates you from the other maths youtubers out there. Keep it up papa flammy!

[wallacealbert]

AMAZING VIDEO BOI, greetings from Brazil.

[heczr]

these kind of maths make me laugh my ass off, whenever a teacher says shit like "why dont we multply this with q!"

[matteodamiano]

E but it's flammable maths and not markiplier

[kamilbizon]

This video was pefrect. Easy to understand and amount of memes wasn't overwhelming

[dgrandlapinblanc]

Sympathetic video. Small error at 8'09" with the inequality. Thank you very much.

[dannygjk]

I knew this wasn't going to be easy for my old, out of practice brain.

[HCOSzifon]

17:12 – it's certainly not rational. The "head" (e - tail) is rational, because it's a sum of rationals, however e itself is irrational, therefore the tail, equal to e - head, is irrational too. A more correct yet still sufficient statement would be to say that the tail is strictly greater than 0 and strictly less than 1, so it can't be an integer.