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#26 2012-02-21 04:52:30
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
well yeah,but the problems in high school are almost always solvable,at least for regular program of teaching.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#27 2012-02-21 04:56:58
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
That is true and it is very dangerous.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#28 2012-02-21 04:57:47
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
i think i know why you think so.for the same reason you fear simplification. 
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#29 2012-02-21 04:59:27
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#30 2012-02-21 05:01:45
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
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?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#31 2012-02-21 05:03:20
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
What exactly are you trying to do with it?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#32 2012-02-21 05:09:36
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
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 (2012-02-21 05:53:14)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#33 2012-02-21 05:14:40
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
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?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#34 2012-02-21 05:21:25
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
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.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#35 2012-02-21 05:24:40
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
Hi anonimnystefy;
That is what I am not quite getting. I need some explanation on what you did there.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#36 2012-02-21 05:31:01
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
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.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#37 2012-02-21 05:34:55
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
That is what I do not understand. You used parameters a and b?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#38 2012-02-21 05:37:47
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
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.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#39 2012-02-21 05:48:32
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
Okay, look at post #32. The piecewise is not defined for lots of points.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#40 2012-02-21 05:53:01
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi bobbym
it's not defined only -1 and 1.the zero is accidental.i shall edit my post.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#41 2012-02-21 05:58:23
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
I am going to bring it down here:
-1 and 1 have no definition for them. You want it like that?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#42 2012-02-21 06:06:01
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
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.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#43 2012-02-21 06:15:39
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
I have the graph looking like this:
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#44 2012-02-21 06:23:50
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi bobbym
that's exactly it.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#45 2012-02-21 07:04:47
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
I am not seeing how to get those line segments into one form.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#46 2012-02-21 07:54:42
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi bobbym
found it:The function
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#47 2012-02-21 08:23:34
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
Isn't that a 3D plot?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#48 2012-02-21 09:08:16
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
i don't know how you got 3D.it's the graph of y=sgn(x+1)+sgn(x-1).
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#49 2012-02-21 09:10:31
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
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.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#50 2012-02-22 01:41:08
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi bobbym
i don't know if you know,but sgn function is not defined at 0.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón