# Cardinality of Infinite Sets

## Homework Statement

Prove that the union of c sets of cardinality c has cardinality c.

## The Attempt at a Solution

Well, I could look for a one-to-one and onto function... maybe mapping the union of c intervaks to the reals, or something? I know how to demonstrate that a countable union of countable sets is countable, by showing how to label them.
I'm having a hard time with this one, though.

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AKG
$$\mathbb{R}^2 = \bigcup _{r \in \mathbb{R}} (\mathbb{R} \times \{ r\} )$$