The first number set we learned as children was the set of natural or counting numbers. This is also true in the history of humans; early humans first counted the objects around them. Observe a small child (maybe a three year old) when the child is learning to count. What would the child do when counting the collection of insects illustrated below?

       Most small children would point at each insect and say each number as the child counts the insects. We illustrate below by drawing a correspondence between the insects and the numerals 1 through 12.

       After finishing the child may say that there are 12 insects.

       This example indicates there is a correspondence between the collection of insects and the first twelve counting numbers. This motivates the introduction of the two concepts:  set and one-to-one correspondence.