Proposition 13

Let $\mathfrak{a}$ and $\mathfrak{b}$ be cardinals. Then $\mathfrak{a} \geqslant \mathfrak{b}$ if and only if there exists a cardinal $\mathfrak{c}$ such that $\mathfrak{a} = \mathfrak{b} + \mathfrak{c}$.

For the relation $\mathfrak{a} \geqslant \mathfrak{b}$ means that there exists a subset B of $\mathfrak{a}$ which is equipotent to $\mathfrak{b}$ (no. 2), i.e., $\mathfrak{a}$ is equipotent to the set which is the sum of $\mathfrak{b}$ and a set $c$.

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If $\mathfrak{a} \geqslant \mathfrak{b}$, there usually exist many cardinals $\mathfrak{c}$ such that $\mathfrak{a} = \mathfrak{b} + \mathfrak{c}$ (cf. § 6); in general, therefore, it is not possible to define the "difference" $\mathfrak{a} - \mathfrak{b}$ of two such cardinals (cf. § 5, no. 2).