is there a 1-1 MAP in N and all prime numbers?

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# is there a 1-1 MAP in N and all prime numbers?

Submitted by lilianjie8836 on Mon, 07/18/2011 - 13:29

Forums:

123456.........

2,3,5,7,11.....

some books :because all prime numbers no exist a formula,so can not 1-1 MAP N...

who can give a 1-1 MAP?

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## Versions

(v1) by lilianjie8836 2011-07-18

## Re: is there a 1-1 MAP in N and all prime numbers?

thank you very much!

Bernstein Theorem can get Both sets have the same cardinality

but isomorphism'define:bijection 1-1 map ----->isomorphism.

the bijection need a prime numbers formula:

N----------->P

n|---------->prime numbers formula

is isomorphism only use for finite set?

## Re: is there a 1-1 MAP in N and all prime numbers?

You don't need a formula for prime numbers for the existence of such a map. It suffices to know that the set of (positive) prime numbers is an infinite subset of the countable set N. Both sets have the same cardinality.