Math Basics

All About Numbers

What is meant by one-to-one correspondence?

A one-to-one correspondence means as the words imply: that the number of objects, numbers, or whatever is the same as the set of other objects, numbers, or whatever. (In set theory, the one-to-one correspondence means something different; for more about set theory, see “Foundations of Mathematics.”)

Everyone has no doubt had contact with one-to-one correspondence without even thinking about it. For example, there is a one-to-one correspondence of the number 10 to the number of fingers on both hands (ten). Counting a deck of cards is a one-to-one correspondence—each number, from 1 to 52, representing a card in the deck. When you compare two decks of cards, putting the cards side-by-side to equal 52 in each deck, this could also be considered a one-to-one correspondence.

Not everything is counted in such a way. For example, when mathematicians want to know the size of an unknown quantity, they put the unknown quantity in a one-to-one correspondence with a known quantity.


This is a web preview of the "The Handy Math Answer Book" app. Many features only work on your mobile device. If you like what you see, we hope you will consider buying. Get the App