Re:0.999...= 1
by tom-thistime on Tuesday April 28, 2020 @10:49AM
(#23007517)
This is a really good point. Maybe the problem is how we define equality. What's the test for when two numbers are equal?
People accept that 1/3 = 0.333333... The same people don't always seem to accept that 3*0.33333... = 1. Well, how are we defining "equals"? If we can give that definition in black and white, I think that may help.
> What's the test for when two numbers are equal?
I put this in another comment but: For the reals: eliminate a < b and a > b then conclude a = b.
So using that as a foothold, we can express 1/3 + 1/3 + 1/3 as 0.333… + 0.333… + 0.333… and it should be pretty easy to digest. At once we can see that in this little zone we've defined, 1 and 0.999… mean the same thing.
Not a rigorous proof, and one or two people will probably bring up whataboutisms like "that's just because the calculator can't do stuff!" but it should at least be proof of comfort for most people.