This wiki is incomplete.
This is part of a series on common misconceptions.
True or False?
There are infinitely many numbers in the interval
Why some people say it's true: Every new combination of digits after "0." leads to a new number between 0 and 1. Since there are infinitely many possible combinations, there are infinitely many numbers in .
Why some people say it's false: Since the length of the interval is finite, there can't possibly be infinitely many numbers in .
The statement is .
Proof: The fraction will always be in the interval for all positive integers . Since there are infinitely many positive integers, there are infinitely many numbers in the given interval.
Rebuttal: (Address any concerns that people have)
Reply: (Explain why the argument is not vald)
(If relevant, add in an example problem that demonstates understanding of this misconception.)