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Epsilon-delta procedure

In standard analysis, epsilon-delta procedures are used to avoid infinitesimal numbers.


Example 1

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.


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