Textbook Problem

A set is finite if, and only if,________

To determine

To fill:

A set is finite if, and only if, _____.

Answer to Problem 1TY

A set is finite if, and only if, it is the empty set or there is a one-to-one correspondence from $\left\{1,2,\dots ,n\right\}$ to it, where n is a positive integer.

Explanation of Solution

Given information:

The given statement is,

“A set is finite if, and only if, _____”.

 A set is called a finite set when it is either an empty set or the process for counting of elements definitely comes to an end.

Thus, a set is finite if, and only if, it is either an empty set or there is a one-to-one correspondence from $\left\{1,2,\dots ,n\right\}$ to it, where n is a positive integer.