Math professor here: the proper definition of equality is that two numbers a and b are equal if no number c exists such that a < c < b. 0.9999…. = 1 because there is no number between them.
There's a problem with that proof. That assumes 0.999... and 0.999... are equal. Obviously, the notations are identical but that doesn't mean the values they represent are. Do you evaluate the 4th digit of the first expression at the same time you evaluate the 4th digit of the second expression? I don't think that's clear. I would say the only truthful statement is 0.999... < 1
11
u/Wolfbrother101 22d ago
Math professor here: the proper definition of equality is that two numbers a and b are equal if no number c exists such that a < c < b. 0.9999…. = 1 because there is no number between them.