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Limits are something the human race (at least, the mathematicians) have created as a result of trying to find a way to think about infinity.

Another way of thinking about infinity involves things called infinitesimals. An infinitesimal is a number that's bigger than 0, but smaller than all normal everyday fractions. If ε is an infinitestimal, then

...

...

and yet,

0 < ε.

This website has a great discussion of limits and infinitesimals.

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