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## Homework Statement

Let S be the set consisting of all sequences of 0's and 1's.

S = {(a_1, a_2, a_3,...):a_n = 0 or 1 }

Show that S is uncountable.

## Homework Equations

## The Attempt at a Solution

I'm not sure where to start. I think I should either assume that S~N and use proof by contradiction. Or maybe I could show that S has the same cardinality with R which means there is a bijective map between those two. Both of them don't seem easy.

I would really appreciate it if anyone could show me where to start.