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functions [2015/12/16 13:13] nikolaj |
functions [2015/12/16 13:16] 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. | + | == Many definitions are implcit == |
| + | Caution: | ||
| + | Many function definitions are implicit, sometimes secretly so. E.g. defining | ||
| - | 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. | + | $f(x):=\sum_{n=0}^\infty\frac{(-1)^{3n}}{n!}z^n$ |
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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. | ||
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| + | == Practically speaking, uor functions are partitially defined == | ||
| + | Caution: 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. | ||
| In that sense, "Functions" really is "Partial functions", a priori, although I try to state good valid domains on AoC. | In that sense, "Functions" really is "Partial functions", a priori, although I try to state good valid domains on AoC. | ||
