###### Example1.5.5Determine if Numbers are This Type or That Type

Determine which numbers from the set \(\left\{-102, -7.25, 0, \frac{\pi}{4}, 2, \frac{10}{3}, \sqrt{19}, \sqrt{25}, 10.\overline{7} \right\}\) are natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.