Cardinality of Natural & Positive Even Numbers

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The discussion confirms that the set of natural numbers and the set of positive even numbers have the same cardinality, meaning there exists a bijective function between them. It is noted that a function from natural numbers to natural numbers excluding odd numbers would not be surjective. The correct approach is to establish a bijection that maps each natural number to a positive even number. The concept extends to any set of natural numbers defined by a consistent interval, such as every nth natural number, which also shares the same cardinality. Thus, the cardinality of natural numbers and positive even numbers is indeed equivalent.
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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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