# Definition:Dedekind-Infinite

## Definition

A set is said to be **Dedekind-infinite** if and only if it is equivalent to (at least) one of its proper subsets.

## Also see

- Infinite Set Equivalent to Proper Subset
- Equivalent Conditions for Dedekind-Infinite Set
- Galileo's Paradox

## Source of Name

This entry was named for Julius Wilhelm Richard Dedekind.