Quote:
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.
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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.