# What does the broken vertical bar ¦ mean?

I have a question which I am unable to solve because I don't know what the broken vertical bar ¦ stands for:

If $\mathbf a\cdot \mathbf b = \mathbf a\cdot \mathbf c$ where $\mathbf a ¦ \mathbf 0¦\mathbf b$, what conclusion(s) can be made?

Any ideas what the symbol means?

• From en.wikipedia.org/wiki/… : The broken bar has hardly any practical application and does not appear to have any clearly identified uses distinct from the vertical bar. In non-computing use — for example in mathematics, physics and general typography — the broken bar is not an acceptable substitute for the vertical bar – fosho Mar 1 '16 at 17:59
• This doesn't explain what it means in this context. – Richard Smith Mar 1 '16 at 18:05
• Looks like the definition of an integral domain: $a\neq 0$, $a \cdot b = a \cdot c$ implies $b = c$. – Luis Vera Mar 1 '16 at 18:05
• Can you tell us the source (book, notes, website, etc) of this notation? – pjs36 Mar 1 '16 at 18:12