# What does bR mean in relation to all real numbers?

I was working on learning some terms for math analysis when I came upon the following problem: Suppose a is a ﬁxed real number.

The negation of $\exists x\in\mathbb R(x>a)$ is equivalent to $\forall x\in\mathbb R \lnot(x>a)$ .

From the properties of inequalities, this is equivalent to $\forall x\in bR(x \leq a).$

My question is, what exactly does $bR$ mean in this context and how is it spoken? I gather that the first statement is, 'for all x in the set of all real numbers, there is no x greater than a'. I just haven't seen that alternate definition.

As a note, I'm not great at mathjax so in the second block, both of the R's should be the 'all real numbers R' and the bR is in italics.

• That doesn’t look like anything to me. Probably a typo, and bR should just have been the real numbers $\mathbb{R}$. – Mankind Jun 20 '18 at 18:50
• Looks like a typographic error. If you change $bR$ to $\mathbb R$ then the last statement becomes equivalent to the second one. – David K Jun 20 '18 at 18:53
• Probably tried to do \Bbb R and goofed it. – Cameron Williams Jun 20 '18 at 18:58
• On the plus side, if you try to “edit” the question now you’ll see how to do a bunch of symbols in MathJax. – David K Jun 20 '18 at 19:00
• I would guess the author defined his own macro \bR and forgot the backslash. – Hans Lundmark Jun 20 '18 at 19:09

For example, let's suppose someone frequently uses this typeface: $\Bbb N,$ $\Bbb Z,$ $\Bbb Q,$ $\Bbb A,$ $\Bbb R,$ $\Bbb C,$ $\Bbb{ON}.$ (Feel free to ask me what any/all of these typically mean.) Well, rather than having to make $4$ or more keystrokes every time they want to use this typeface, TeX allows one to preprogram macros to make it happen quickly.