How did Richard Dedekind define an infinite set?

Richard Dedekind defined an infinite set by utilizing the concept of one-to-one correspondence, a technique he adopted from the work of Bernhard Bolzano.1

In his 1888 work, Was sind und was sollen die Zahlen? ("What Are and Should Be the Numbers?"), Dedekind established that a set is infinite if and only if the entire set can be put into a one-to-one relationship with a proper part (a subset) of itself. This definition provides a precise mathematical criterion for identifying sets that are not finite, distinguishing them by their ability to map onto their own components without exhausting the original collection.21