(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Question 1:

Prove that the cardinality of R (the set of all real numbers)is the same as the cardinality of R-{0} by constructing a bijective function from R to R-{0}

Question 2: Let A be the infinite sequence of binary numbers as follows:

A={(a1,a2,a3...)|ai= 0or 1 for all i in the natural numbers}

Show that A is uncountable

2. Relevant equations

3. The attempt at a solution

For question 2 I think I have to use a proof similar to Cantor's diagonalization argument for proving that the set of real numbers is uncountable. I think I have to use contradiction and assume that the set is countable.

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# Math Proof: Uncountable binary sequence and a bijection from R to R-{0}

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