(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**