Originally Posted by
Jani
1/3 cannot be written as an exact decimal.... .33333repeating is an Approximation.
proofs lose validity when you approximate.
limit of .9999 = 1, but .9999 != 1
repeating decimals are not approximations in any way, they are exact
here is my mth491 book
numbers: rational and irrational
by: ivan niven
pay attention to problem set 8, number 1, part f
the last pic is the solutions in the back of the book
problem set 8, number 1, part f
from this i conclude that writing .999 repeating as a fraction is exactly 1
thus .999... = 1