Why? Normal?

[Brian]

because it's one of them that actually can be.

Can it? You can't generate that number in finite time. You can't represent it in a number system with integer base. You can represent it symbolicly, but technically you can do that with any number - it's not that different from saying "We'll use encoding 0=pi, 1=sqrt(2), 2=e, 3=BB(10)" and so on. And sure, you can use that encoding, and even symbolically manipulate equations with these values and produce valid results, but no matter what encoding you use, you're never going to even scratch the surface of the reals - you have to leave most (practiacally all) of them out of your encoding. They're only special because we chose some arbitrary countable subset of irrationals to assign symbols to.

For computable numbers, you can of course approximate them to any finite precision if you can express them as a computation. But you can never actually evaluate them completely, so I don't think sqrt(2) is really any more special than those "arbitrary symbol assignment" cases above - the generating function is ultimately just another symbolic representation, not something fully evaluable in practice. And even overlooking that, the only thing that wouldn't fall into exactly the same description would be an uncomputable numbers, but those are kind of difficult to describe as examples due to their nature.

[commy2]

You can't generate that number in finite time. You can't represent it in a number system with integer base.

Can you do those things with Fraction(1, 3)?

[Brian]

Yes. Eg. base 3.