Definition:Set Equivalence

Two sets $$S$$ and $$T$$ are equivalent iff there is a bijection between the elements of $$S$$ and those of $$T$$.

This can be written $$S \sim T$$.

If $$S$$ and $$T$$ are not equivalent we write $$S \not \sim T$$.

Some authors use the term equipotent. Others use the term similar.