/sci/ - Science & Math

>>9435725
>As the Mediterranean diet usually includes products containing gluten like pasta and bread, increasing use of the diet may have contributed to the growing rate of gluten-related disorders

>>9265572
[math]a-b = (\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})[/math]
and
[math](\sqrt[2^n]{a}-\sqrt[2^n]{b})=(\sqrt[2^{n+1}]{a}+\sqrt[2^{n+1}]{b})(\sqrt[2^{n+1}]{a}-\sqrt[2^{n+1}]{b})[/math]

therefore by induction:
[math]a-b = \prod\limits_{i=1}^{\infty}(\sqrt[2^{i}]{a}+\sqrt[2^{i}]{b})\times\lim\limits_{i\rightarrow \infty}(\sqrt[2^{i}]{a}-\sqrt[2^{i}]{b})[/math]

observe that
[math]\lim\limits_{i\rightarrow \infty}(\sqrt[2^{i}]{a}-\sqrt[2^{i}]{b})=0[/math]

hence
[math]a-b=\prod\limits_{i=1}^{\infty}(\sqrt[2^{i}]{a}+\sqrt[2^{i}]{b})\times0 = 0[/math]

meaning that
[math]a=b \quad \forall a,b\in\mathbb{R}[/math]