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A sequence of numbers x1x2x3, ...  has a limit L if the numbers in the sequence are arbitrarily close to L.



A definition of a limit is:

If, given any ε however small, there is a number δ > 0 such that for 0 < δ < δ0, the absolute value of the difference (f (x0 ± δ) – L) is less than ε, then L is the limit of (f (x0 ± δ) – L) for x0.

Here is no mention of infinitely small quantities. They have no place in mathematics.



The Bohemian mathematician Bernard Bolzano (1781 - 1848) developed this definition.

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