Talk:Loss of significance

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The page reads:

'Examples of ill-conditioned calculations are:

• Subtracting two almost equal numbers
• Division by almost zero

In these ill-conditioned calculations you get errors which tend to blow up dramatically. '

Division by a small non-zero number does not result in loss of significance. It may (depending on the numerator) cause numerical overflow, as may multiplication, addition, or subtraction. This is a very different and separate problem from loss of significance.

Subtraction of almost equal numbers is the sole source of loss of significance.

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The formula given for loss of significance gives undefined results for x < y. Is "assuming x > y" missed out, or should it be abs(1 - y / x)?