Q(x, z) = "x has z followers on Twitter"
Universe of discourse for x, y = all students Universe of discourse for z = non-negative integers
How would I properly write the following in English?
$$\forall y \exists x \; Q(x,y)$$
I know $$\forall x \exists y \; Q(x,y)$$ would be: everyone has at least one follower on Twitter. The inverted variables is what's confusing me.
Assuming that the universe of discourse for $x$ is ‘all students’, and for $y$ is the non-negative integers...
As you say, $\forall x \exists y Q(x,y)$ means ‘for every student $x$, there is some $y$ which is the number of followers $x$ has on Twitter’. More naturally, this is ‘all students have a (non-negative integer) number of followers on Twitter’.
$\forall y \exists x Q(x,y)$ could be translated as ‘for all non-negative integers $y$ there exists a student $x$ who has $y$ followers on Twitter’. More naturally, this is ‘For any non-negative integer, there is a student who has this number of followers on Twitter’. So, for example, there is a student with $3$ followers. There is also a student with $5378245$ followers. The same goes for all other non-negative integers.