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functions [2015/12/16 13:13] nikolaj |
functions [2015/12/16 13:14] nikolaj |
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| === Discussion === | === Discussion === | ||
| - | Caution 1: Man function definitions are implicit, sometimes secretly so. E.g. defining $f(x):=\sum_{n=0}^infty\frac{(-1)^{3n}}{n!}z^n$ is defining $f(x):=\lim_{m\to\infty}\sum_{n=0}^m\frac{(-1)^{3n}}{n!}z^n$ and a Limit definition is always a Task to find said limit. | + | Caution 1: Man function definitions are implicit, sometimes secretly so. E.g. defining |
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| + | $f(x):=\sum_{n=0}^\infty\frac{(-1)^{3n}}{n!}z^n$ | ||
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| + | is defining | ||
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| + | $f(x):=\lim_{m\to\infty}\sum_{n=0}^m\frac{(-1)^{3n}}{n!}z^n$ | ||
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| + | and a Limit definition is always a Task to find said limit. | ||
| Caution 2: In the function Definition, the domain of the function, as well as variables in context, are stated quite broadly - it must be checked if the to-be-function would return a value for any given input. | Caution 2: In the function Definition, the domain of the function, as well as variables in context, are stated quite broadly - it must be checked if the to-be-function would return a value for any given input. | ||
