Question

. Let f : Z → N be function. a. Prove or disprove: f is not...

. Let f : Z → N be function.
a. Prove or disprove: f is not strictly increasing. b. Prove or disprove: f is not strictly decreasing.


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Answer #1

we know that Z and N are are two countable unbounded set. The set N is bounded below and least lower bound is 1. If the mapping is strictly increasing then the least element of Z is connected with 1 in N by the map. But least element of Z does not exist since Z is unbounded below. So the map is not strictly increasing.

Similarly we can say that the map is not strictly decreasing  because if the map is strictly decreasing then the element 1 in N is connected with the largest element of Z but largest element of Z does not exist as Z is unbounded above.

So two statements is true.

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