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.