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.

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

People who frequently use a particular symbol or typeface will often come up with macros, to reduce the number of characters that they have to type.

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.

The above examples don't necessarily illustrate the utility as well as it might. I'll draw from personal experience to give a slightly better one. At one point, I let "\di(integrand,variable,lower bound,upper bound)" be a shortcut for "\int_{lower bound}^{upper bound}integrand\,d variable."

At any rate, I concur fully with Hans Lundmark that the person typesetting the text forgot a "\" in their setup.


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