Question

Discrete Math Prove that Z has no smallest element.

Discrete math
ANSWERED
asked 2021-08-20
Discrete Math
Prove that Z has no smallest element.

Expert Answers (1)

2021-08-21

Step 1
we will prove it by contradiction,
Suppose x belongs to Z is the smallest element.
Step 2
Now, consider an element \(\displaystyle{\left({x}-{1}\right)}\) from the set Z,
As, \(\displaystyle{\left({x}-{1}\right)}{<}{x}\), so x can not be the smallest element now, which results into a contradiction,
Hence, Z has no smallest element.

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