# Large Intro

Finally submitted my first assignment. It was monstrous. Just over 23 pages of mathematics and sketches of graphs. All of it typed up in LaTeX. Skipping ahead to look at the rest of the assignments, it looks as if this first assignment may very well be the biggest of the whole lot. This is a very good thing as I really don't think I could churn out that much work of a high quality every month.

Glad to say that most of this introduction section I was familiar with. Only really new topic was equivalence relations, which caused some problems initially.

Overall though, what I've found difficult is the apparent lack of logical notation. After reading "How To Prove It" I've become half-decent at making sense of and rearranging logical notation to solve a problem. The difficulty comes in looking at the plain-English description of something in the texts and then having to translate it into logical notation to allow my fussy brain to think about them logically.

Perfect example of this is the definition of a function being "onto". In the text, the definition reads:

"A function $f: A \longrightarrow B$ is onto if $f(A)=B$".

Which is fine, but the Wikipedia definition reads:

"$\forall y \in Y, \exists x \in X$ such that $y = f(x)$"

Which for me, gives me a much better idea about how to go about proving if a function is onto. Why leave out the quantifiers? The Wikipedia definition tells me so much more. I suppose translating English into logical notation is just something I'll have to get good at!

Though even after this long intro section, I really feel I need more practise with proofs... I guess this may have to wait until revision time... Next up is the first section on group theory, with an assignment due on November 24th. Onward.