Hi everyone,

I wanted to give an example of writing a given set in set-theoretic notation – this should help out with some of the problems on your first homework assignment (Section 1.1).

**Example:** Write in set-theoretic notation:

In this case, you can see that the given set consists of all multiples of 5. A good way to approach problems like this is to start with one of the basic sets, for example

- the natural numbers
- the integers

In this example, I can see that multiplying every natural number by 5 should give me the set that I want. Therefore, I will use the formula , and the condition . Combining these in set-theoretic notation gives the solution:

**Solution**

Here are two ways to read this solution aloud:

- “the set of all such that is a natural number”, or
- “for each in the natural numbers, multiply by and include the result in the set”

I hope this helps – feel free to respond here if you any questions.

Best,

Prof. Reitz