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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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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**benice****Member**- Registered: 2010-06-10
- Posts: 110

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: 15,525

hi benice

thank you!

now i just need to find the general formula.

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**benice****Member**- Registered: 2010-06-10
- Posts: 110

anonimnystefy wrote:

hi benice

thank you!

now i just need to find the general formula.

y = 0.5 (a sgn(x + 1) + b sgn(x - 1))

*Last edited by benice (2012-02-21 11:00:20)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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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**benice****Member**- Registered: 2010-06-10
- Posts: 110

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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**benice****Member**- Registered: 2010-06-10
- Posts: 110

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: 15,525

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: 3,562

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: 86,705

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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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**benice****Member**- Registered: 2010-06-10
- Posts: 110

anonimnystefy wrote:

just wondering,you wrote there three formulas ....

The third one is a general formula.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Hi benice

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

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

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**benice****Member**- Registered: 2010-06-10
- Posts: 110

anonimnystefy wrote:

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

f and g are arbitrary deterministic (non-random) functions.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Deterministic?

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,562

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: 15,525

You're welcome!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Hi bobbym

And that is?

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**benice****Member**- Registered: 2010-06-10
- Posts: 110

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: 86,705

Hi anonimnystefy;

And that is?

Sometimes Sgn, Signum or Sign.

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,705

Hi;

Welcome to the forum!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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