I have a function that I as a programmer would express like this in pseudo-code:
myFunc(int[x0, x1, ... xn]){
return 1/((1/x0)+(1/x1)+...+(1/xn));
}
How is this expression written in a mathematical form?
Asked
Active
Viewed 66 times
0
-
What happens if you input $x_0=0$? – Dan Rust Dec 21 '13 at 16:30
-
That is undefined. – Alex Dec 21 '13 at 16:33
-
Then mathematicians would not call this a function (unless you restrict to the domain on which it is defined). – Dan Rust Dec 21 '13 at 16:43
-
How would you specify a limitation like this in the below provided answers? – Alex Dec 21 '13 at 17:07
-
@RossMillikan Thanks, I misread the post and removed the answer. Unfortunately, typos tend to generate more downvotes than solutions of hard problems generate upvotes. – AD - Stop Putin - Dec 22 '13 at 11:10
2 Answers
0
AD's answer is slightly incorrect... your function would be written as $$f(x_0,\ldots,x_n) = \frac{1}{\sum_{k=0}^n \frac{1}{x_k}}$$ or perhaps $$f(x_0,\ldots,x_n) =\left(\sum_{k=0}^n x_k^{-1}\right)^{-1}.$$
Notice also that it is very closely related to the harmonic mean.
user7530
- 49,280
-
Because of the missing inversion, right? And your two examples is equal for all inputs, just a different way to express the same mathematical relation? – Alex Dec 21 '13 at 17:05
-
0
Let $A\subset(\mathbb{Z}\setminus\{0\})^{n+1}$ be defined as $$A=\left\{(x_0,\ldots,x_n)\in(\mathbb{Z}\setminus\{0\})^{n+1}\mid \sum_{i=0}^n x_i^{-1}\neq 0\right\}$$ and let $f\colon A\to\mathbb{R}$ be given by $$f(x_0,\ldots,x_n)=\left(\sum_{i=0}^n x_i^{-1}\right)^{-1}.$$
This takes in to account that one of the above questions isn't defined on its assumed domain (either the $(n+1)$-fold cartesian product of the integers, or the product of the integers without zero. The above function is actually well defined - that is, every element in its domain is mapped, by $f$, to a unique, well-defined element in the codomain.
Dan Rust
- 30,108