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0: The basics

Last updated

Nov 6, 2021
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- Using the exercises in this book
- 0.1: Numbers

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We won't make this section of the text too long — all we really want to do here is to take a short memory-jogging excursion through little bits and pieces you should remember about sets and numbers. The material in this chapter will not be (directly) examined.

0.1: Numbers
Before we do anything else, it is very important that we agree on the definitions and names of some important collections of numbers.
0.2: Sets
All of you will have done some basic bits of set-theory in school. Sets, intersection, unions, Venn diagrams etc etc. Set theory now appears so thoroughly throughout mathematics that it is difficult to imagine how Mathematics could have existed without it.
0.3: Other Important Sets
We have seen a few important sets above — namely $\mathbb{N}, \mathbb{Z}, \mathbb{Q}$ and $\mathbb{R}\text{.}$ However, arguably the most important set in mathematics is the empty set.
0.4: Functions
Now that we have reviewed basic ideas about sets we can start doing more interesting things with them — functions.
0.5: Parsing Formulas
Consider the formula
0.6: Inverse Functions
There is one last thing that we should review before we get into the main material of the course and that is inverse functions.

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