This is an observation in abstractmath that I think needs to be publicized more:

Two symbols used in the study of integers are notorious for their confusing similarity.

- The expression “$m/n$” is a
**term** denoting the number obtained by dividing $m$ by $n$. Thus “$12/3$” denotes $4$ and “$12/5$” denotes the number $2.4$.
- The expression “$m|n$” is the
**assertion** that “$m$ divides $n$ with no remainder”. So for example “$3|12$”, read “$3$ divides $12$” or “$12$ is a multiple of $3$”, is a *true* statement and “$5|12$” is a *false* statement.

Notice that $m/n$ is an integer if and only if $n|m$. Not only is $m/n$ a *number* and $n|m$ a *statement*, but the statement “the first one is an integer if and only if the second one is true” is correct only after the $m$ and $n$ are switched!

## math, language and other things that may show up in the wabe