Haiku: My Favorite Number

$\text{One nth, but a third won't do}$ $\text{x is half n, that much is true}$ $\text{So n squared must be two!}$ $\text{And x, I won't forget you}$ $\text{Because you are half n, } \sqrt{2}/2!$

First and foremost, one $n$ th is simply $\frac{1}{n}$ , like how one tenth is $\frac{1}{10}$ , one eleventh is $\frac{1}{11}$ , etc.

$\frac{1}{n}=x=\frac{n}{2}$ $\implies \frac{1}{n}=\frac{n}{2}$ $2=n^2$ $n=\pm \sqrt{2}$

This means that $|x|=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\approx .7071$ $\beta_{\lceil \mid \rceil}$

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Personal note : This is my favorite number for multiple reasons. Firstly, it is simultaneously half of a number and the inverse of that same number (as seen in the middle of the last equation; it's a simple yet cool identity). Secondly, it appears in trigonometry and complex algebra very frequently ( $\sqrt{i}\approx \pm(.7071+.7071i)$ ; $\sin (\frac{\pi}{4})=\cos (\frac{\pi}{4})\approx .7071$ ). Lastly, it is very dear to me because it is a testament to how, not just in mathematics, there is no singular correct way to express and idea or solve a problem.

1/n = n/2 n = square root of two. Therefore X = 0.7071