Cardinality of Natural & Positive Even Numbers

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SUMMARY

The set of Natural numbers and the set of all positive even numbers possess the same cardinality, confirming that a bijective function exists between them. The proposed function, f:N->N - {n | n=2x-1}, effectively excludes odd numbers, establishing a one-to-one correspondence. This principle extends to any set of every nth natural number, which also maintains the same cardinality as the set of Natural numbers.

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srfriggen
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correct me if I'm wrong, but the set of Natural numbers and the set of all positive even numbers have the same number of elements, the same cardinality, right?

So there would have to be a bijective function between the two, correct?

If we go from f:N->N then the function is not surjective, since all the odd numbers are being left out.

So would the correct function be, f:N-> N - {n,x in N l n=2x-1} (the latter set being the natural numbers minus the odd numbers)
 
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srfriggen said:
correct me if I'm wrong, but the set of Natural numbers and the set of all positive even numbers have the same number of elements, the same cardinality, right?

So there would have to be a bijective function between the two, correct?

I believe that is correct. It would be true even if you took the set of every 10th natural number since the set of every nth natural number has the same cardinality as the set of all natural numbers.
 

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