(December 13, 2015 at 4:20 pm)IATIA Wrote:(December 13, 2015 at 2:59 pm)Quantum Wrote: If you disagree with 0.99999...=1, you have no business talking about algebra and calculus
Then they can be substituted for each other in all cases which is false, but that would be an argument for a different thread, though it would not progress any further than "there is a god / there is no god". Been there, done that.
I'm with Quantum. Give us an example of where substituting them doesn't work.
0.999... Is equal to 1. Most people who don't accept this probably don't know know what mathematicians mean when they say that. It doesn't mean the numbers are the same, because of course they are different numbers, but the value which the number represents is the same.
Just like 2/2 is equal to 1. Different numbers, same value.
If you think 0.999... and 1 are different values, then there must be a value which lies between them. What is it? Try as hard as you can, you won't be able to find another value which fits between 0.999... and 1, therefore they are the same value.
Another way to think about it is this:
1/3 = 0.333...
Multiple each side by 3.
3 x 1/3 = 3 x 0.333...
1 = 0.999...
