Quantifier/Examples/Definition of Greater Than or Equal To
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Example of Use of Quantifiers
Let $x$ and $y$ be in the natural numbers.
- $\forall x: \forall y: \exists z: y \ge x \implies y = x + z$
means:
- If a natural number $y$ is not less than a natural number $x$, then $y - x$ is a natural number.
Sources
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.1$: The need for logic: Exercise $(7) \ \text{(ii)}$