Im struggling to understand whether the relation "is a permutation of" on N+
Relations on N+, that show specific properties.
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2I assume you mean 'sequences of natural numbers of length at least one' by 'N+'? What are your intuitions for those properties you mentioned? What have you tried and where are you struggling? – 2012-12-12
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Hint: Go back to the definition. For symmetry, if you have a list of numbers $a_n$ such that $a_n\ R \ \mathbb N+$, is it also true that $\mathbb N+ \ R \ a_n$? You are given that for any given $k$, there is a unique $p$ such that $a_p=k$ from the definition of permutation. For anti-symmetry, can you show a permutation of $\mathbb N+$ that is not the identity? For reflexitivity, is your list a permutation of itself? For transitivity, given two permutations, can you compose them?
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0@yatima2975: I was thinking "is a permutation of $\mathbb N^+$" in all cases. For reflexivity and transitivity, I think all you have to say is that if two lists $a_n$ and $b_n$ have every number once and only once, they are related. – 2012-12-12