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functions [2015/12/14 10:34] nikolaj |
functions [2015/12/16 13:16] nikolaj |
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=== Discussion === | === Discussion === | ||
+ | == Many definitions are implcit == | ||
+ | Caution: | ||
+ | Many function definitions are implicit, sometimes secretly so. E.g. defining | ||
- | 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. | + | $f(x):=\sum_{n=0}^\infty\frac{(-1)^{3n}}{n!}z^n$ |
+ | |||
+ | 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. | ||
+ | |||
+ | == 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. | ||
== todo == | == todo == | ||
- | Is there any reason to generalize $\to$ (as in $A\to{B}$, fucntion type) to $\prod$ (as in $\prod_{a:A}B(a)$, i.e. dependent product type) here? | + | Is there any reason to generalize $\to$ to $\prod$ here? I.e. going from $A\to{B}$ (function type) to $\prod_{a:A}B(a)$ (dependent product type). |
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=== Related === | === Related === | ||
[[Domain of discourse]] | [[Domain of discourse]] |