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Originally Posted by daking
Here you make the mistake of accepting the notation of 1/infinity as valid. It is not valid or correct notation, it makes no sense.
In such cases it does pay to consider convergance. Consider
y=sin(x)/x
at x = 0, we have y=0/0 which is undefined. But ofcourse by the limit as x tends to zero is 1 by l'hopitals rule .
See if you can work out what the limit is as x tends to infinity  |
The limit is zero.
Notation is often defined by the person employing it, how can it be invalid in this instance? Certainly the concept of one divided by infinity comes up daily in the study of calculus. The limit of 1/x as x approaches infinity can be thought of as 1/infinity, which by the definition of limit is zero. 1/infinity = 0