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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

well yeah,but the problems in high school are almost always solvable,at least for regular program of teaching.

Here lies the reader who will never open this book. He is forever dead.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

That is true and it is very dangerous.

**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: 15,507

i think i know why you think so.for the same reason you fear simplification.

Here lies the reader who will never open this book. He is forever dead.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

Worse than that. It subtly puts into the students mind that all problems have solutions by the standard methods.

**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: 15,507

thought so.i know you fear general thought.

i think we are going a little bit off-topicy-ish here.so what do you say about the three piece piece-wise functions?

Here lies the reader who will never open this book. He is forever dead.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

What exactly are you trying to do with it?

**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: 15,507

hi bobbym

did you even read my question back then?

if i wanted to represent the next function with only one formula,how could i do that? :

*Last edited by anonimnystefy (2012-02-20 06:53:14)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

Yes, I read it but I do not understand it. The purpose of the piecewise notation is to represent functions that can not be represented by one equation, so why are you going backwards?

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: 15,507

hi bobbym

well it may not always be true.

e.g. look at my first post.i showed that the piecewise function:

can be represented with a single formula,so i'm guessing other ones can too.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

Hi anonimnystefy;

That is what I am not quite getting. I need some explanation on what you did there.

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: 15,507

hi bobbym

i started by looking at the graph of y=sgn(x) for all x<>0 where sgn(x) represents the sign function valued +1 for positive values of x and -1 for negative values of x.

then i saw that if we scale and/or translate that graph we get similar graphs where the only thing that changes are the starting points of the two rays.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

That is what I do not understand. You used parameters a and b?

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: 15,507

hi bobbym

if you are wondering what a and b represent in the first place,then i will explain myself.a and b represent the y coordinates of the starting points of those two rays.in my example a=3 and b=1.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Okay, look at post #32. The piecewise is not defined for lots of points.

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: 15,507

hi bobbym

it's not defined only -1 and 1.the zero is accidental.i shall edit my post.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

I am going to bring it down here:

-1 and 1 have no definition for them. You want it like that?

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: 15,507

hi bobbym

yes,that's right.it's easier to find a formula for that one that for the one where -1 and 1 are included.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

I have the graph looking like this:

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: 15,507

hi bobbym

that's exactly it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

I am not seeing how to get those line segments into one form.

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: 15,507

hi bobbym

found it:The function

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

Isn't that a 3D plot?

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: 15,507

i don't know how you got 3D.it's the graph of y=sgn(x+1)+sgn(x-1).

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

Over there it is written as y sgn(x+1)+sgn(x-1).

Also that equation has a value at 1 and -1. Your piecewise does not.

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: 15,507

hi bobbym

i don't know if you know,but sgn function is not defined at 0.

Here lies the reader who will never open this book. He is forever dead.

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