Abstract Algebra I · Groups, subgroups, and generated structures
Why subtraction is not a group law
Problem
On $\mathbb Z$, define $a\star b=a-b$. Decide whether $(\mathbb Z,\star)$ is a group. Give explicit witnesses for every group axiom you claim fails.
Hint
Compare $(0\star0)\star1$ with $0\star(0\star1)$.
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