Hi everyone,

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

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

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

- Â 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. Â Therefore, I will use the formula , and the conditionÂ . Â 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 youÂ any questions.

Best,

Prof. Reitz