possible revision to 9.7.6 to avoid confusion

[DorusKeijzer]

Some of my students have difficulties parsing 9.7.6:

They read it as if x is negated, rather than the element function: "for every x, the negation of x is an element of the empty set", rather than "for every x, x is not an element of the empty set".

Could this be resolved by explicitly using parentheses? so: ∀x¬(x ∈ ∅) or using prefix notation? ∀x¬∈(x, ∅).

I personally had no good way to explain why this is the way to read it other than showing the prefix version. I understand that for these more "mathetmatical" expressions, both seem a bit unnatural, but it would save some time and confusion on the students' part.

another aside: Throughout the entire lecture notes, the succesor function is written with a capital S, which disagrees with the convention that functions should be lowercase letters. At first I didn't think much of it because I know that it's the most common way of writing the successor function in mathematics, but yesterday someone handed in homework where they tried to (and of course, failed to) apply the semantic rules of of a predicate to the succesor function. I understand that it's a pretty tall order on my part to ask to replace this and any wary student who thinks about what it says rather than mindlessly applying rules should know that this is a function and should be treated as such, but still it led to some unncessary confusion.

[jkorb]

Thanks @DorusKeijzer . Agreed. I'll introduce parentheses in the official infix notation.

[jkorb]

About the successor function. Well, that's a tougher one: it's 100% standard to have a capital S for the successor function, and students need to get used to that. From a more technical perspective, it's perhaps also important to get used to the idea that functions can be written in all sorts of ways.