# Why there is no sign of logic symbols in mathematical texts?

Either in undergraduate or graduate textbooks on Mathematics (Real/Complex Analysis, General Topology, Differential Geometry, …), I never saw symbols $\Rightarrow$, $\iff$, $\forall$, $\exists$, etc. Instead, I just see their “read as” or explanation such as “if … then …”, “if and only if”, “for all”, “there exists”, etc. Before I started to study mathematics, I thought I would see a lot of logical symbols, but I didn’t see any (even once!) even in the proofs. Why is that so? If they are for mathematical use and they take less space in texts, why are there none of them in mathematical textbooks?

Let us fix any $\epsilon>0$. It follows from the assumptions that there exists a positive number $\delta$ with the property that $1/x<\epsilon$ whenever $x>\delta$
$(\forall \epsilon>0)(\exists \delta>0)(\forall x)(x > \delta \Rightarrow 1/x<\epsilon)$.