Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
37 followers · 119 posts · Server mathstodon.xyzA beautiful proof of why \(\sqrt{2}\notin\mathbb{Q}\):
Let \(k=\min\{n\in\mathbb{N}:n\sqrt{2}\in\mathbb{N}\}\).
But, \(k(\sqrt2-1)\sqrt2=2k-k\sqrt2\)
and \(k(\sqrt2-1)<k\).
\(\implies\boxed{\sqrt2\notin\mathbb{Q}}\)
#irrationality #squareroot2 #beautifulproof #maths #mathematics #numbers #irrationalnumber #irrational
#irrational #irrationalnumber #numbers #mathematics #maths #beautifulproof #squareroot2 #irrationality
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
37 followers · 119 posts · Server mathstodon.xyzA beautiful proof of why \(\sqrt{2}\notin\mathbb{Q}\):
Let \(k=\min\{n\in\mathbb{N}:n\sqrt{2}\in\mathbb{N}\}\).
But \(k(\sqrt2-1)\sqrt2=2k-k\sqrt2\) & \(k(\sqrt2-1)<k\).
\[\implies\boxed{\sqrt2\notin\mathbb{Q}}\]
#irrationality #squareroot2 #beautifulproof #maths #mathematics #numbers #irrationalnumber #irrational
#irrational #irrationalnumber #numbers #mathematics #maths #beautifulproof #squareroot2 #irrationality