# Why are Set Cardinality and Absolute Value denoted the same way?

When we have a set $A$, it is conventional to denote the cardinality of $A$ as $|A|$. When we have some number $n$, it is conventional to denote the absolute value of said number as $|n|$.

My question is whether there's any 'deeper' reason for this: is there some mathematical connection between the two concepts that explains why the two operators are denoted the same way?

We tend to use bars to denote some concept of 'size', whether it be cardinality, absolute value, determinant, or a norm. For cardinality, other accepted notations include $\#A$ and $card(A)$.

• Also Cantor's notation for cardinality, $\overline{\overline A}$. – bof Nov 11 '13 at 16:36
• @bof I think that notation might have fallen out of favour with modern authors, but yes that's another alternative :). – Dan Rust Nov 11 '13 at 16:49
• Fair enough - I usually use $\#(A)$ to denote set cardinality to avoid ambiguity. – Newb Nov 11 '13 at 17:45

For a finite set S, its cardinality (being a non-negative integer) is sometimes denoted by 𝑛S, or at least it was when I was in primary (junior) school in the 1970's.