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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

Hi anonimnystefy;

That is not correct. It is defined for 0.

Sign[0] = 0.

Here is how it is defined in Wikipedia.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

hi bobbym

really.oh well.we can take it one the same interval just excluding the zeors of the functions.so for the last function which has three parts we would look at it just over the R\{-1,1}

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anonimnystefy wrote:

found it:The function

Hi anonimnystefy;

It's a nice expression!

Here is another expression: y = 0.5 sgn(x) (1 + sgn(abs(x) - 1)).

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

hi benice

thank you!

now i just need to find the general formula.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

hi benice

thanks for that formula as well.but i wanted the formula which will give the three lines at hights of a,b and c,respectively.

if you find anything let me now.once again,thank you for the formulas.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

hi benice

i think i found one,but i don't know if it works for all heights and distances:

where a,b and c are the heights i mentioned and d and e are the distances of the breakings in the interval or in other words, d and e are the points where the sgn(x) function breaks according to our 'definition'.

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anonimnystefy wrote:

hi benice

i think i found one,but i don't know if it works for all heights and distances:

where a,b and c are the heights i mentioned and d and e are the distances of the breakings in the interval or in other words, d and e are the points where the sgn(x) function breaks according to our 'definition'.

Assume d < e.

x<d

=> y = 0.5[(a+c) + (b-a)(-1) + (c-b)(-1)] = 0.5[a+c-b+a-c+b] = a

d<x<e

=> y = 0.5[(a+c) + (b-a)(1) + (c-b)(-1)] = 0.5[a+c+b-a-c+b] = b

x>e

=> y = 0.5[(a+c) + (b-a)(1) + (c-b)(1)] = 0.5[a+c+b-a+c-b] = c

*Last edited by benice (2012-02-22 14:09:21)*

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Hi anonimnystefy;

You can use the **sgn** function to generate curves with dashed line:

x = sgn(cos(32t)) cos(t)

y = sgn(sin(32t)) sin(t)

x = sgn(cos(512t)) [cos(t) + sin(2t)]

y = sgn(sin(512t)) [sin(t) - sin(2t)]

x = sgn(cos(nt)) f(t)

y = sgn(sin(nt)) g(t)

*Last edited by benice (2012-02-22 14:35:57)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

hi benice

now those are some nice graphs.thanks for sharing that.

just wondering,you wrote there three formulas,and there are two graphs.which formula is for which graph?

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,566

what is this "sgn" function? Can you provide a definition of it.

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

Hi John;

A few examples will do the trick:

sign(0) = 0

sign(+5) = 1

sign(+.3) = 1

sign(-2) = -1

sign(-200.34) = -1

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

hi JEF

it's called the sign function.and as its name says,it gives us the "sign" of the number.for positive numbers it returns 1, for negative -1 and for 0 it returns zero.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Hi benice

I don't know why I didn't notice it.

Are f(t) and g(t) random functions?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Deterministic?

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,566

thanks for the examples (bobby) and definition (anom).

**igloo** **myrtilles** **fourmis**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

You're welcome!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

Hi John E. Franklin;

Your favorite programming language might have that command built in.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Hi bobbym

And that is?

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Hi anonimnystefy;

Here is a more general formula:

f(x) = 0.5 {f1(x) + f3(x) + sgn(x-a)[f2(x) - f1(x)] + sgn(x-b)[f3(x) - f2(x)]}

anonimnystefy wrote:

Deterministic?

http://en.wikipedia.org/wiki/Deterministic_system

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

Hi anonimnystefy;

And that is?

Sometimes Sgn, Signum or Sign.

While python and C++ do not, mathematica, maple, delphi, Maxima and VB do.

**In mathematics, you don't understand things. You just get used to them.**

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**afridinazneen****Member**- Registered: 2012-03-20
- Posts: 1

I have gotten some good information here.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,638

Hi;

Welcome to the forum!

**In mathematics, you don't understand things. You just get used to them.**

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