Infinite Set

Facts

In ZFC Set Theory, Dedekind-infinite $\iff$ Infinite under

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$\varnothing$ is a finite set

A set containing an infinite set is infinite

Every subset of finite set is finite

for bijective function $f:X\to Y$, If $X$ is an infinite, then $Y$ is also infinite If $X$ is a finite, then $Y$ is also finite

If the subset of an infinite set, $X\subset Y$ is finite, then $X-Y$ is infinite