# Weak Inequality of Integers iff Strict Inequality with Integer plus One

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## Theorem

Let $a, b \in \Z$ be integers.

The following statements are equivalent:

- $(1): \quad a \le b$
- $(2): \quad a < b + 1$

where:

- $\le$ is the ordering on the integers
- $<$ is the strict ordering on the integers.

## Proof

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