# Is this set uncountable

by Bachelier
Tags: uncountable
 P: 376 ##S = \bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i ## methinks yes because: ##S = \bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i \equiv \left\{{0,1}\right\}^\mathbb{N}##
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P: 15,934
 Quote by Bachelier ##\bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i \equiv \left\{{0,1}\right\}^\mathbb{N}##
This equality is false. Furthermore, the set on the right is uncountable. The set on the left is countable.
P: 376
 Quote by micromass This equality is false. Furthermore, the set on the right is uncountable. The set on the left is countable.
So how do we look at ##\left\{{0,1}\right\}^∞##?

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P: 15,934

## Is this set uncountable

 Quote by Bachelier So how do we look at ##\left\{{0,1}\right\}^∞##?
What do you mean with $\infty$? The notation you are using now is not standard at all.
 P: 90 I think that $S = \bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i$ is countable all right. The mapping with $\mathbb{N}$ is quite obvious.