Sound and Fury

Signifying nothing

Problem solved. Also wow!

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This is ridiculous. Productive day I’ve been having, watching videos on youtube…

My friend Tom explained how there are uncountably many mltiplicative subsets of the natural numbers;

CONSIDER the countably infinite set of prime numbers, and its uncountable power set. By taking a relevant element of that power set you can generate any multiplicative subset you want; additionally since prime factorisations are unique, distinct elements will generate distinct multiplicative subsets, hence you have a 1-1 correspondence with an uncountable set.

QED!

So there we go.

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Written by Seamus

May 26, 2007 at 2:55 pm

Posted in maths

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