universal quantifier

let $\text{[math]}$ be a relation and let $\text{[math]}$ be a variable, the expression $\text{[math]}$ means "for each $\text{[math]}$ , $\text{[math]}$ is true"

consider the sentence "for every x, M(x)"
it can be written as $\text{[math]}$ or $\text{[math]}$
how about "for every real number x, M(x)"? $\text{[math]}$

the universal quantifier is an abbreviation for for all.
[cite:@jaynes_prob_2003 chapter 1.8.2 nitpicking]