Thread: Binary Representation of Real Numbers

1. Binary Representation of Real Numbers

Hey everyone,

I have question that is asking to show that the set of real numbers has no binary representation. I understand that real numbers cannot have a one to one correspondence with natural numbers. I also understand that the real numbers are an uncountable infinity and natural numbers are a countable infinity. I am a bit lost on how to use this information to prove this. Can anyone help me make the connection?

Thanks

2. What do you mean by a binary representation of a set (of real numbers)?