Continuum has Cardinality of Continuum

Theorem

Let $\CC$ be a continuum, including continuum in the topological sense.

Then the cardinality of $\CC$ is equal to the cardinality of the continuum.

That is: all continua have the same cardinality.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continuum: 2. (plural continua)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continuum: 2. (plural continua)