# Which R to use to indicate the real numbers? [closed]

In general, when people are talking about set of real numbers, they usually use one of the following notations:

$$\tag{1} x \in R.$$ $$\tag{2} x \in \textbf{R}.$$ $$\tag{3} x \in \mathbb{R}.$$ $$\tag{4} x \in \Re.$$

I understand that it might be convient to use one notation over the other (e.g. when the letter $R$ assigned a different meaning already, like a region of integration).

However I am curious whether there is an actual distinction between the notation, like a historical reason, or is it just preference which notation to use?

The last one seems to be used quite often as wel..

• No (4) used for real part of a complex number. Jan 7, 2017 at 10:38
• In Operations Research (4) is used a lot to specify the real numbers.
– user394255
Jan 7, 2017 at 10:39
• @Glasses, one would more conventionally use \Re instead of \mathfrak R tho. Jan 7, 2017 at 10:40
• @J.M.isn'tamathematician thanks didn't know that shortcut :) !
– user394255
Jan 7, 2017 at 10:42
• There is no right choice. It's about context, and as long as the reader is aware of the meaning of the symbol it's fine. In set theory you can find $\Bbb R$ used for denoting a forcing poset quite often. Jan 7, 2017 at 11:01

Nr. (1) usually used for a region in analysis, and is a ring in algebra also,

Nr. (2) not conventional in new mathematical books for reals. Some people use Bold characters for vectors, like A, B, ...

Nr. (3) is the best character, preferred by many mathematicians. This character specific number sets like $\mathbb{R}$ for real numbers, $\mathbb{C}$ for complex numbers, $\mathbb{Q}$ for rationals, $\mathbb{Z}$ for integers, $\mathbb{N}$ for natural numbers, and so on. It is the best character for this purpose.

Nr. (4) designed for real part of a complex number in computer editors, but mathematicians don't used it vastly. They used bold $Re$ (Re) instead of it.

it is $$\mathbb{R}$$ the right sign

• goodlike answer (+1)! Jan 7, 2017 at 10:50

I prefer $\mathbf{R}$ in print, leaving $\mathbb{R}$ for writing on paper or blackboard.

It's an aesthetic choice, also made by Serre and Knuth for instance:

https://en.wikipedia.org/wiki/Blackboard_bold

See a discussion at

• In StackExchange one uses $\Bbb R$, as Dr. Sonnhard Graubner indicates (a competitive sick has put him a downvote). Jan 7, 2017 at 10:49
• I use $\Bbb R$ here too, to avoid noise.