Help with set builder notation

Question

I want to express the following set using set builder notation: '{x | x is the square of an integer and x < 100}',

My attempt : $\{ a \in \mathbb Z \mid x = a^2 \land x < 100 \}$.

Is this correct?(I don't know how to type the epsilon and and symbol on my computer)

Answer 1

Your set is read as:

The set of integers $a$ whose square $x$ is less than $100$.

which equals $\{-9,-8,\ldots,8,9\}$, which isn't what you wanted to encode. Minor modifications can make your definition work - you just need to think about what you need to say. Firstly, you need to say that $a$ itself is less than $100$, whereas you have that something else is less than 100. Secondly, you need to say that $a$ is the square of something, not that something is the square of $a$.