(March 1, 2018 at 1:42 pm)polymath257 Wrote:(March 1, 2018 at 1:41 pm)SteveII Wrote: Nope. The fact that we assign 1 to 0.99999... is a convenience in mathematics.
What you are really saying is 1 = 1 - 1/infinity.
Since 1/infinity does not equal zero, then 1 does not equal 0.99999...
Nope that is NOT what the symbolism means. It is not just a convenience. Those are actual, exact, equalities.
I assure you, you don't want the technical definition. You wouldn't be able to handle the logic of the definition.
What you have then is a limit of mathematics to account for the difference. It would mean the two are mathematically equivalent. This does not mean that the two are logically equivalent.
When we are talking about spanning infinite series of things (as in Zeno's paradoxes) we are decidedly NOT talking about mathematics.
And don't tell me next that mathematics and logic are the same thing. https://en.wikipedia.org/wiki/Logic#Types