Confusion on notation in the definition of reflexivity. This is a very silly question i assume to most of you but how would I read this
$\forall x \in X : (x,x) \in R$
I don't quite know what the colon indicates and this definition is used to define reflexivity .
Thanks in advance.
It is a hold over of the dot notation used in Principia Mathematica, which has mainly been replaced by bracketing.   It is basically just a punctuation mark to visually separate the quantifier's restriction from its scope. $$\forall x\in S:P(x)\\\forall x\in S~\big(P(x)\big)\\\forall x\in S~P(x)$$
Normally the colon is read as &quot;such that&quot;
∀ ∈  :(,) ∈ 
For all $x$ in {the set} X such that $(x,x)$ {$x$ maps to itself} in {the binary relation} R {which is a subset of X}.