Realizability in mathematics

Question

What does it mean in mathematics when someone says "it is realizable"? If someone could give me a general and intuitive explanation I would appreciate it. Thank you!

Answer 1

If one lets $X$ be an object with a list of properties $P_1,P_2,\ldots,P_n$, say, then it may not be apparent that an $X$ exists which satisfies these properties. If there is such an $X$, we say $X$ is realizable, otherwise $X$ is not realizable.

A baseball home plate is not realizable (link), since the required lengths and angles cannot be simultaneously achieved (it requires the existence of a right angled triangle with side lengths $12$, $12$ and $17$).