Deep theorem with trivial proof [closed]

It is the snobbishness of the young to suppose that a theorem is trivial because the proof is trivial.

Henry Whitehead

I have been awestruck by the beauty of this quote.

What is in your opinion a good contender to exemplefy the meaning intended by Whitehead?

Off the top of my head I am thinking of Langrange’s theorem in Group Theory, which is rather simple to prove but provides a very useful insight.

Answer

Cantor’s diagonal argument shows not only the completely unintuitive result that uncountable sets exist, but that something as everyday as the real numbers belongs to that category.

The proof may be explained even to those with no mathematical background by a simple drawing.

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nbubis

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