why is the set of all integer powers of 2 {2^x|x is in z} is denumerable

Then why is the set of all prime numbers denumeralbe

and explain why the number of points on a circle is denumerable or uncountable

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- December 13th 2008, 03:32 PMmathcncdenumerable vs uncountable
why is the set of all integer powers of 2 {2^x|x is in z} is denumerable

Then why is the set of all prime numbers denumeralbe

and explain why the number of points on a circle is denumerable or uncountable - December 13th 2008, 03:39 PMJhevon
we can find a bijective function from the naturals to the set. so it has the same cardinality as the naturals.

or better yet, since the integers are denumerable, it suffices to find a bijection from the integers to the set, which would be a bit easier to describe. the desired result follows by transitivity

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Then why is the set of all prime numbers denumeralbe

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and explain why the number of points on a circle is denumerable or uncountable

- December 23rd 2008, 06:02 PMHallsofIvy
There exist the obvious mapping x->2^x and there is a well known mapping from N to Z: f(n)= n/2 if n is even, -(n+1)/2 if n is odd.

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Then why is the set of all prime numbers denumeralbe

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and explain why the number of points on a circle is denumerable or uncountable