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We were discussing bounded and unbounded sets in class, and looking over my notes, I see that I have some trouble understanding the concept.

Here are three examples that our professor gave us:

Set A = {x[tex]\in[/tex]R | |x| <10}

Set A = {x[tex]\in[/tex]R | x<10}

A[tex]\subseteq[/tex]Z s.t. x~y iff x|y

Set A = {1,2,3,4,5,8}

Supposedly the first one is bounded, the second one is not, and the third one has a lower bound of 1 but does not have an upper bound.

I just genuinely don't understand why this is the case...anyone care to explain?

Thanks so much!