[smac__]

Each time I hear the argument, that real numbers between zero to one are a "larger" (nuanced) infinity than natural numbers, I want explore and see if it is possible to make a one to one mapping between these sets. This post is my attempt. It was a fun thought experiment.

[GTP]

Interesting approach, but it has been proven by mathematicians (I'm not one) that the cardinality of the set of the real numbers between 0 and 1 is the same as the set of all the real numbers. I would suggest discussing your approach and your doubts with a mathematician, as when talking about infinities there is a lot counterintuitive stuff going on. Another commenter already pointed out a possible problem of your "mirror" method: you're relying in being able to read a number backwards. To do that, you need to know all the digits. But it doesn't work well with numbers with infinite decimal digits like pi or its inverse.

[smac__]

> I would suggest discussing your approach and your doubts with a mathematician

Great point, this is my attempt to do that. Truly, it may be an inefficient means, but it seemed like a simple approach. Also, it is fun, even when I am wrong. It means I get to learn something new and see from a different angle.

> Another commenter already pointed out a possible problem of your "mirror" method: you're relying in being able to read a number backwards. To do that, you need to know all the digits. But it doesn't work well with numbers with infinite decimal digits like pi or its inverse.

True, this is a glaring flaw in the current reasoning.

Thank you for the thoughtful response!

[onesphere]

If real numbers are more applicable to reality, then computer science should look for all the ways to calculate these numbers. Would this look like a “path integral” of real numbers?