Poll: What Type of Number Would You Want to Be? (I think I got it to work this time.)

[Chronos]

The set of all numbers that can be finitely expressed in any notation system is a countable set. Put the notation in a PDF file (or any other convenient computer file), and each of those PDF files corresponds to an integer, so the number of expressible numbers can be no greater than the number of integers.

[Senegoid]

@Hari_Seldon

Yes. Mathjax is essentially a subset of LaTeX. I’m not sure how far it goes. Simple equations for sure.

Wowie Zowie! Now we can re-hash all those 0.999...=1 threads with real mathematical notations!

(Note, the real-time preview pane acts real clunky when there’s any of this in the post.)

[Ynnad]

@Chronos

The set of all numbers that can be finitely expressed in any notation system is a countable set. Put the notation in a PDF file (or any other convenient computer file), and each of those PDF files corresponds to an integer, so the number of expressible numbers can be no greater than the number of integers.

This sounds like a good start. Now if we could show: (1) the set of “non-expressible” numbers is a noncountable set and (2) a noncountable set is larger than a countable set, I think we are there. It seems obvious but how do we know for sure?

[74westy]

0.000...1

[Hari_Seldon]

@Ynnad

This sounds like a good start. Now if we could show: (1) the set of “non-expressible” numbers is a noncountable set and (2) a noncountable set is larger than a countable set, I think we are there. It seems obvious but how do we know for sure?

The problem with this argument is that there could be uncountably many representation schemes. Both e and \pi can be expressed with a single well-understood symbol.