We call a set $X$

• Dedekind-infinite if there is an injective map $f:X\to X$ that is not surjective,
• addiditvely infinite if $X \neq\emptyset$ and there is an injective map $f:\big((X\times\{1\})\cup(X\times\{2\})\big) \to X$, and
• multiplicatively infinite if $X$ contains $2$ different points and there is an injective map $f:X\times X \to X$.

In ${\sf (ZF)}$, multiplicative infiniteness implies additive infiniteness, which in turn implies Dedekind infiniteness.

Are some or all of these definitions equivalent in ${\sf (ZF)}$?

We call a set $X$

• Dedekind-infinite if there is an injective map $f:X\to X$ that is not surjective,
• addititvely infinite if $X \neq\emptyset$ and there is an injective map $f:\big((X\times\{1\})\cup(X\times\{2\})\big) \to X$, and
• multiplicatively infinite if $X$ contains $2$ different points and there is an injective map $f:X\times X \to X$.

In ${\sf (ZF)}$, multiplicative infiniteness implies additive infiniteness, which in turn implies Dedekind infiniteness.

Are some or all of these definitions equivalent in ${\sf (ZF)}$?