> Well, you can describe a negative number or a rational number, but an infinite sequence of non-repeating decimals is a different matter. I'm a bit confused..

> Well, you can describe a negative number or a rational number, but an infinite sequence of non-repeating decimals is a different matter. I'm a bit confused... it sounded like you had objections to defining numbers with infinite decimal expansions, but you're okay with e, pi, etc? Or did you just object to uncomputable reals? Also I don't know much about this whole topic, but I was taught that you can't fill a continuous line with just the rational numbers – you need the "undefinable" ones for that... What do you think about this? Also thanks for the references, I might check them out to see what Wildeberger has to say.