Could it be possible to come up with a formula or infinite series or continued fraction to generate the real numbers? I might have to change something in my formula to generate another real. I couldn't just change one of my numbers in the formula because then i would be saying there is a one-to-one correspondence between the naturals and the reals and there isn't. But what if I used irrational numbers to change my formula or something like that. And i don't think we could generate the reals in order because there is no next real on the number line, maybe its not possible, what do you guys think.