Why Set Symbols have a line with the alphabets?

Question

I was wondering that all the set symbols I have seen have a vertical line with them. e.g. the set of Real Numbers is represented by $\mathbb{R}$ this so why is there this line with the R. Can anybody answer?

Answer 1

Historically, well before TeX, it was common for the set of real numbers and the set of integers to be handwritten as the letters R and Z, respectively, with a double line in them, something like this:

The purpose was to identify these as "global constants" (although using that term from computer science is an anachronism), and to leave, for example, the unadorned letter R to be free for use to denote a relation.

As I recall, in print these were often just typeset as $\mathbf{R}$ and $\mathbf{Z}$ in regular boldface; the double-line versions were an attempt to simulate this boldface in handwritten symbols.

The double-line handwritten style was particularly common in blackboard use by professors, so the computer font in TeX inspired by this is called "blackboard bold".

By the way, one would occasionally see letters other than R or Z given this double-line treatment, but I don't believe those others were used as commonly; blackboard bold in TeX has become much more standardized, with such symbols as $\mathbb{Q}$ and $\mathbb{C}$ in very common use and understood throughout the math community.