It depends on the context.
If this is part of a piece of text, then you might consider Peter Grill's suggestion:
$\exists a\in\mathbb{R}$, $\exists b\in\mathbb{R}$,
$\forall c\in\mathbb{R}$, and $\forall b\in\mathbb{R}$
On the other hand, if the quantifiers are part of a logical formula, you might consider a dot between the quantifiers, like this:
$\exists a\in\mathbb{R}\ldotp\exists b\in\mathbb{R}\ldotp
\forall c\in\mathbb{R}\ldotp\forall b\in\mathbb{R}\ldotp P$
This dot notation is inherited, I think, from Russell and Whitehead's Principia Mathematica, and is quite widely used, particularly in computer science. A comma between quantifiers is quite unusual, though it does appear in the syntax of the Coq theorem prover.
$\exists a\in\mathbb{R}, \exists b\in\mathbb{R},
\forall c\in\mathbb{R}, \forall d\in\mathbb{R}, P$
The comma notation becomes awkward when you want to quantify several variables at the same time, because then you have two different types of comma in the same formula:
$\exists a,b\in\mathbb{R}, \forall c,d\in\mathbb{R}, P$
In such cases, you might consider putting just a space between the variables, like this:
$\exists a\;b\in\mathbb{R}, \forall c\;d\in\mathbb{R}, P$
The idea of putting spaces between variables, rather than commas, is taken from the syntax of the Isabelle theorem prover.
Best Answer
Hard to comment on efficiency (one of your tags) without knowing more context.
\footrue
and\foofalse
are really each just a\let
. So if the only reason that this token is let to one definition or another is so that you can decide whether or not to "do stuff" then you don't need the if token at all, then you don't need the test.Just define
then you can replace the
\iffoo
construct with simplyand it will either do nothing or the real definition depending on whether
\foofalse
or\footrue
was most recently executed. Since this saves expanding\iffoo
and skipping over the conditional text it is more efficient in principle but whether the difference is measurable on modern machines I haven't checked. It is unlikely that any of these make any real difference unless you do (literally) millions of tests.