Looking online I can see that W is used for the Whole numbers, but I never saw the W symbol used in all my math classes.

Personally I learned that 0 was a natural number and looking online it is said that 0 was not included in the original definition, but was later added. To avoid mistake, N* is often used to indicate that it contains 0. At the end, it's not really that important but it's good to know !

Tbf I started really understanding calculus once I was in Uni; I'm now studying engineering and I can integrate in my sleep lol

> integrating by parts

I guess it's a calculus class ? Good luck with that, it was dreadful for me; I had to do the class 3 times before passing the class lol

If you didn't know, Z, Q and R are also used. Z are for the integers (-inf to +inf) while N are the natural numbers (0 to +inf). Q is for the rationnal numbers, all the numbers that can be written as a quotient a/b where b isn't equal to 0 (you also have Q' for the irrationnals like pi). Finally R are for the reals. It's important to note that each categorie can contain some of the other categories. For example, all natural numbers are integers, and all integers are real.

EDIT : As commented below, apparently 0 isn't included in N, but in N* (Natural numbers including 0) or W (Whole numbers). Didn't learn it that way, but maybe some people did ?