(March 4, 2012 at 3:11 pm)LastPoet Wrote: As to why, I've already outlined it in that post, its the numbering system we use that allows for more than one different representation for the same number. For instance, in the rational number, 1 has infinite fraction representations, e.g. 1/1, 2/2, 3/3,...,n/n.
Oh, I understand. But while I can see that 2/2 obviously equals one, and that 4/2 equals two, I don't see (at this point, probably because I don't understand a lot of the principles of mathematics yet) how 0.999* = 1. I understand that you can write the same number in different ways, but it seems to me that 0.999* is standing for a different idea than 1. But (if there really is mathematical consensus here) I'm sure that's just because I don't understand enough of the principles of math to see why 0.999* clearly equals one, in the way that 2/2 so clearly equals one.
So you're saying understanding the concepts of "dense and countable sets" would help me see clearly why 0.999* and one are the same thing? If so, if it's not too much trouble of course, would you be able to link me to an explanation (of dense and countable sets, and any other mathematical concepts that would help me understand) that is pretty accessible to a layperson?
