How can I prove that the set of all positive integers is not bounded above
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How can I prove that the set of all positive integers is not bounded above

[From: ] [author: ] [Date: 13-10-31] [Hit: ]
n.Then by definition, there is no member of Z q such that q>n.But by definition of Z+, if z belongs to z then the successor of z belongs to Z+ (or z + 1 belongs to Z+).So n has a successor (or n+1 belongs to Z+).......
I suppose I'd do proof by contradiction but this is one of those proofs that seems so obvious that I have a hard time knowing where to start. I know it's a countably infinite set, so how can I formally show that there cannot be an upper bound?

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I don't know how your class formally defined the integers or bounded from above. here is how I would do it:

Suppose Z+ has an upper bound, n.
Then by definition, there is no member of Z q such that q>n.
But by definition of Z+, if z belongs to z then the successor of z belongs to Z+ (or "z + 1 belongs to Z+").
So n has a successor (or "n+1 belongs to Z+).
But by definition of ">" the successor of n is greater than n, so we have a contradiction.
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