Cardinality of \mathbb{R}^{\mathbb{N}} - Is it \mathbb{R} or \{0,1\}?

jostpuur · 2010-06-02T13:05:13+00:00

What's the cardinality of \mathbb{R}^{\mathbb{N}}? It must be \mathbb{R} or \{0,1\}^{\mathbb{R}}, but I'm not sure which.

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Start date Jun 2, 2010
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jostpuur

Thread starter
Jun 2, 2010

What's the cardinality of [tex]\mathbb{R}^{\mathbb{N}}[/tex]?

It must be [tex]\mathbb{R}[/tex] or [tex]\{0,1\}^{\mathbb{R}}[/tex], but I'm not sure which.

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Hurkyl

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Jun 2, 2010

Arithmetic to the rescue!

R^N = (2^N)^N = ...

Cardinality of \mathbb{R}^{\mathbb{N}} - Is it \mathbb{R} or \{0,1\}?

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