Epic Proof Moments

[Anonymous No.14683667]

>that moment when the [math]4^n[/math]s cancel in the proof of the Cauchy Integral Formula

[Anonymous No.14684381]

>>14683667
I remember that moment.

[Anonymous No.14686726]

tmw u tell god that he should strike you down if hes real because hes a big poopy head and nothing happened thereby disproving god

[Anonymous No.14687483]

Why does nobody like my thread :(
Almost like you're a bunch of fakers who don't actually know any epic proof moments :(

[Anonymous No.14687528]

[math]

\delta \, \epsilon \left ( 0,1 \right ) \\
\displaystyle
\prod_{k=0}^{n} \left ( 1 + \delta ^{2^{k}} \right )
= (1+ \delta)(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
(1- \delta) \prod_{k=0}^{n} \left ( 1+ \delta ^{2^{k}} \right )
= (1- \delta)(1+ \delta)(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
= (1- \delta ^{2})(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
= (1- \delta ^{4})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}})
= (1- \delta ^{2^{n}})(1+ \delta ^{2^{n}}) = 1- \delta ^{2^{n+1}} \\
\\
\boxed{(\delta ^{2^n})^2 = \delta ^{2 \cdot 2^n}=\delta^{2^{n+1}}}
\\
\displaystyle
\prod_{k=0}^{n} \left ( 1+ \delta ^{2^{k}} \right )
= \dfrac{1- \delta^{2^{n+1}}}{1- \delta} \\
\displaystyle
\lim_{n \to \infty} \prod_{k=0}^{n} \left (1+ \delta ^{2^{k}} \right )
= \lim_{n \to \infty} \dfrac{1- \delta^{2^{n+1}}}{1- \delta} = \dfrac{1}{1- \delta}
[/math]

[Anonymous No.14687855]

>>14687483
It is based, I hope people post more examples. I don't know any epic proofs myself

[Anonymous No.14689277]

>>14687528
That's some good shit.

[Anonymous No.14689384]

Does this count as epic?

[Anonymous No.14690243]

>>14683667
i liked the one about eulers formula where you show e^(i*t)=cos(t)+i*sin(t) with a two-liner

[Anonymous No.14690277]

Epic proof of philosopher retardation