Symbols:Set Theory/Set Equivalence

Set Equivalence

$S \sim T$

Let $S$ and $T$ be sets.

Then $S$ and $T$ are equivalent if and only if:

there exists a bijection $f: S \to T$ between the elements of $S$ and those of $T$.

That is, if and only if they have the same cardinality.

This can be written $S \sim T$.

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

The $\LaTeX$ code for \(S \sim T\) is S \sim T .

The $\LaTeX$ code for \(S \nsim T\) is S \nsim T .

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $14$: Symbols