Originally posted by lao tzu
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My point is that if infinite series is defined for many series though many such series do not reach a convergent limit, then why not so with division?
Especially as I understand that simple division is not defined as an operation with the divisor being a transcendental number; limits are used to define such divisions. Another way I could pose my question is: why then can't division by a real be defined as an operation across the entire real line, ie including 0, by further extending the division operation to zero? Yes, the result is not a convergent limit, but so are the results of many infinite series.
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