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Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.

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Include each point of continuum in a subset so that each subset gets finitely many points

Let $M : = \mathbb R^2 \setminus\{(x, y): x^2 + y^2 \leq 1\}$, $\Delta := \{(x, x) \in \mathbb R^2\}$, and let $h$ be any bijection from $\mathbb R$ to the circle $\{(x, y) \in \mathbb R^2: x^2 + y^2 …
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