# Confusion on equivalence class $[a]=${$(x_a,z);∀z∈C$} meaning

For equivalence class $$[a]=$${$$(x_a,z);∀z∈C$$} means $$[a]=$${$$x_a$$}$$×C$$ where $$z∈C$$. Am I defining it correctly?

• Yes, as you wrote. – user376343 Nov 4 '18 at 21:21
• Though in builder notation I'd rather write $\{\,(x_a,z)\mid z\in C\,\}$ – Hagen von Eitzen Nov 4 '18 at 21:24
• Thanks for confirming this! – BlackSky Nov 4 '18 at 21:25