Is it possible to construct a function out of the elementary (+,-,*,/), the trigonometrical or exponential functions? Or more general, out of basic functions?
I failed on that, I doubt it's possible at all. Greetings Wolfgang Sock
>Is it possible to construct a function out of the elementary (+,-,*,/), >the trigonometrical or exponential functions? Or more general, out of >basic functions?
>I failed on that, I doubt it's possible at all. >Greetings Wolfgang Sock
| little question turned out to be complicated: | | Is it possible to construct a function out of the elementary (+,-,*,/), | the trigonometrical or exponential functions? Or more general, out of | basic functions? | | I failed on that, I doubt it's possible at all.
Well, even if you have failed then it's still possible. :))
Hint: The characteristic function of a positive halfline is
f(x)=(|x|+x)/2x = |if you will | = ((sqrt(x^2)+x)/2x).
On Thu, 30 Sep 1999 12:15:40 GMT, w...@festo.com wrote: >Is it possible to construct a function out of the elementary (+,-,*,/), >the trigonometrical or exponential functions? Or more general, out of >basic functions?
>I failed on that, I doubt it's possible at all.
The closest I can think of is signum(x) = x/(sqrt(x^2)), which is correct except for x=0, where it obviously doesn't work.
In article <7t06ah$s9...@uni00nw.unity.ncsu.edu>, "Oleg V. Poliannikov" <ovpol...@eos.ncsu.edu> wrote:
> | little question turned out to be complicated: > | > | Is it possible to construct a function out of the elementary (+,-,*,/), > | the trigonometrical or exponential functions? Or more general, out of > | basic functions? > | > | I failed on that, I doubt it's possible at all.
> Well, even if you have failed then it's still possible. :))
Hello Oleg,
there you got me! It's amazing seeing the different solutions on a point believing there is no solution. :-0
> Hint: The characteristic function of a positive halfline is
> f(x)=(|x|+x)/2x = |if you will | = ((sqrt(x^2)+x)/2x).
> Oleg*
Nice idea, but it does not really give the function I'm looking for:
The signum-function I'm searching for goes like: sgn(x) = 1 for x>0 sgn(x) = -1 for x < 0 sgn(x) = 0 for x=0
Your function gives: x>0 f(x)=1, ok. x=0 f(x)=?, depends on implementation because of division by 0 problem. normally it's "error because of devison by Null". Rule of "De Hospital" gives 1, am I right? x<0 f(x)= 0 / -2|x| = 0 and not -1.
But it should be possible to modify your function.
What about: g(x)=(|x|+x)/2x + (|x|-x)/2x gives x>0 g(x)= 1 + 0 = 1 => ok. x<0 g(x)= 0 + (-1) = -1 => ok. problem remaining is x=0.
As I told Oleg, it's amazing seeing solutions at a point oneself believes there are no solutions.
One other idea which was directly mailed to is
> What if you took an n-th root of your number, for n odd and very very > large, and took the real root of all the possible nth roots?
> 10^(1/1000000001) is very very close to 1
> -10^(1/1000000001) is very very close to -1
> Yes I do understand that it is not exact. ;)
By using the integer function int(x^1/10000001) that would give correct results, even for x=0. But unfortunately, normally the n-th root with n=big brings problems, especially for x<0 even when n is odd.
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