Proving Inequality relation on integer set.

Question

Let $a,b\in \mathbb{Z}$, Suppose $a<b\;\land a\in\mathbb{Z}^+$. Prove $b\in\mathbb{Z}^+$. I am having trouble using only the axioms of integers.

score 2 · Accepted Answer · answered Mar 28 '17 at 06:07

2

Well, if $a \in Z^+$ then $a > 0$. Since $a < b$, we have $0 < a < b$ by transitive property. Hence, $b \in Z^+$.

answered Mar 28 '17 at 06:07

Yunus Syed

I can't believe it was that simple. I was trying to $b-a>0$ and couldn't find anything. – Alex Mar 28 '17 at 06:11
Initially I thought that because you have b > a and the definition of b > a is b - a > 0. The main trick was realizing that $a \in Z^+$ implies $a > 0$. – Yunus Syed Mar 28 '17 at 06:16

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