I have a set, A = {1,4,9,16,25,36,49,...}, that I want to write a definition for using an elementhood test. I have written one defintion i'm sure is correct but i'm not sure if the other one is appropriate since there are values that satisfy the conditions in the definitions but produce values that are not elements of A.(adsbygoogle = window.adsbygoogle || []).push({});

I have A = { x [tex]\in[/tex] [tex]\aleph[/tex] [tex]^{+}[/tex] | x [tex]^{2}[/tex] }

However I've seen another definition for the same set but i'm not sure it's accurate

A = { x ∈ ℕ [tex]^{+}[/tex] | y is a positive odd integer, x + y }

I'm not sure the second defition is correct, take the case where x is 1 and y is 5, then x+y=6, which is not part of the set. Could someone give me their perspective. I'm under the impression that these definitions have to work in all cases.

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# Definition of set using elementhood test

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