Question

How do you write all the names that apply to `-sqrt100`?

Answer 1

Asking for "all" properties is impossible to fulfil - Anyway, some of the obvious ones are listed below.

Explanation:

Let `x=-sqrt100`

(i) `x in RR`

(ii) `x < 0`

(iii) `x = -sqrt(2^2xx5^2) = -(2xx5) = -10 -> x in ZZ`

(iv) `x^2 = 100`

NB: There are an infinite number of possible properties that could be constructed to define `x` in this example. Understanding that is probably more important than the ones listed above.