FloatingPointRepresentation

Consequently we do not speak of a unique nan value

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Unformatted text preview: do not speak of a unique NaN value but of many possible NaN values. Note that an 1 in the output of a program may or may not indicate a programming error, depending on the context. Addition and subtraction with 1 also make mathematical sense. In the 1 parallel resistance example, we see that 1 + R2 = 1. This is true even if R2 also happens to be zero, because 1 + 1 = 1. We also have a + 1 = 1 and a ; 1 = ;1 for any nite value of a. But there is no way to make sense of the expression 1 ; 1, which must therefore have a NaN value. (These observations can be justi ed mathematically by considering addition of limits. Suppose there are two sequences xk and yk both diverging to 1, e.g. xk = 2k , yk = 2k, for k = 1 2 3 : : :. Clearly, the sequence xk + yk must also diverge to 1. This justi es the expression 1 + 1 = 1. But it is impossible to make a statement about the limit of xk ; yk , without knowing 23 more than the fact that they both diverge to 1, since the result depends on which of ak or bk diverges faster to 1.) Exercise 17 What...
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