On: Converting Pi to binary: Don't do it!

[zyroth]

> There are an uncountably many number of non-normal real numbers like this, even though the infinite amount of normal real numbers is bigger.

How sure are you with that one? Mind to supply a proof?

[kf → zyroth]

I have no proofs; I don't think very many proofs exist with regards to this topic.

From what I've been able to gather, I think the cardinality of the normal and non-normal numbers are the same, even though the non-normal numbers are measurably greater because of probability distributions. This is a paradox that I don't really understand. http://forums.xkcd.com/viewtopic.php?f=3&t=4270

[zyroth → kf]

Anything related to the concept of infinity tends to be hardly understandable in an "emotional" or "intuitive" way. We can just apply the rules of logic and accept.