Question

# Discrete Math Prove that Z has no smallest element.

Discrete math
Discrete Math
Prove that Z has no smallest element.

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.