What ∣ means
The left number divides the right one with no remainder.
So 3 ∣ 12 is true and 5 ∣ 12 is false. In number theory and proofs it usually appears as a ∣ b, read “a divides b.”
Inside braces, as in {n ∣ n > 0}, the bar reads “such that”: the set of all n such that n is greater than 0.
It took hold in the early twentieth century
Edmund Landau, a German number theorist, explained the notation in his 1909 Handbuch, a reference work on how prime numbers are distributed; wider use followed in the 1930s. It replaced a relation previously written out in words with one short sign.
Formal number theory and proof writing; in ordinary chat it signals specialist mathematical notation.
Not ordinary division: 3 ∣ 12 is a yes-or-no claim.
Don't confuse it with
2Questions people ask
1Why does ∣ show as a box on some devices?
Because that device's fonts have no glyph for it. The character is still correct and still copies correctly — the box is a missing glyph, not a broken character.
How to type ∣
∣\2223Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.