tom boosted

THE PRESTIGE:

ok so, the classical proof that
root(2) involves deriving a contradiction from the assumption that root(2) is rational.

however, there is an argument to be made that there is a difference between a number being [not rational], and actually provably belonging to the class of irrational numbers, i.e. quantifiably different in some way from every rational number.

(contd.)

playing with R for the first time

its kind of cool but strange

\[\displaystyle\lim_{R \rightarrow \infty} R \displaystyle\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} e^{it} \log\left( 1 + \dfrac{1}{Re^{it}} \right) \mathrm{d}t\]
\[ = \]
\[ \pi \]

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