0.9 repeating = 1?

[Ether]

Originally Posted by Molten

The limit of a series of partial sums is not equal to the actual sum at all. This is by definition of a limit. A limit is what the function must approach ever closer without ever reaching it. If it ever actual reaches it at any point, then it is not truly its limit.

The meaning of the expression .999... is the sum of the infinite series.

And the sum of the series is the limit of the sequence of partial sums of the series (assuming the limit exists).

The limit in this case exists and is 1, so .999... means 1. They are two different ways of writing the same real number.