Unique

Think of the word unique as being a shorthand for “one of a kind” or “single answer”.

Suppose you are a very young student, and I give you the set

{1, 2, 3, 4, 5}

and then ask you, which number from my set, when added to five, will give a sum of eight?

You think for a minute and then say, “the three”.

“Three” is a unique answer because no other element of the set will do the job correctly, the job being “you must add yourself to five and give back eight”.

We can say 3 is a unique solution to the problem.

If someone asks the question, which element can be added to 2 and the result is less than 6, we see three possibilities so we do not have a unique element or a unique solution.

…

A person may have come to this page looking for logic notation that means “unique”.

The above translates “there exists a unique x”.