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Math Help - Can you help me build a simple formula?

  1. #1
    Newbie Flightline's Avatar
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    Can you help me build a simple formula?

    I'm not in school, and I'm not looking for any answer to any homework assignment. I have something I'm doing on my own, and I wanted to see if anyone comes up with the same formula, or close to it, as I did for the following.

    Take a graph: draw a line so that x=y, which we know is a 45^oangle and a 135^o angle from (0,0) heading in a positive and negative direction on to infinity.

    Now, let's say that the line goes to (1,1) then (2,2) then (3,3) etc. What formula would also extend the line to (-1,-1) (-2,-2) (-3,-3) ...ect., as the line extends positively?

    In other words, you start from (0,0) and the vectors extend positively, and negatively in proportion to each other. When the vector goes from (0,0) to (1,1) to (2,2) it then extends to at the same time to (-1,-1), (-2,-2), etc.

    I understand people have their own work and may not want to be sidetracked with this, but I do appreciate anything anyone has to suggest. My guess is this is a well-known formula, and I'm just don't know well enough to know it. Nevertheless, I want to get this simple formula down before proceeding on with my work.

    Thank you very much in advance for anything.

    Ed
    Last edited by Flightline; July 27th 2010 at 10:10 PM.
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  2. #2
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    Hello !

    The same formula is suitable  \ \ y=x \ \
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  3. #3
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    y=x goes through all the points mentioned above
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  4. #4
    Newbie Flightline's Avatar
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    Thank you, I thought about that, that simply X=Y would do, but that produces an infinite line in both directions. I was looking for a formula, or call it a model, if you will, that indicats that as the line goes to 1,1 it also goes to -1,-1. I have a formula I'd like to show here, but I'm not sure how, just yet. But I will try using TEX, and do a bunch of edits and see what happens. Here it goes:

     <br />
\left(f_(_x_)= x | x=\sum\limits_{n=0}^{\infty}n+1\right)\Longrightar  row \left(f_(_x_)= x | x=\sum\limits_{n=(-1)}^{\infty}n-1\right)
    Last edited by Flightline; July 27th 2010 at 11:12 PM.
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  5. #5
    Newbie Flightline's Avatar
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    OK, above is the formula I have come up with.
    Jeez...talk about a crash course in LaTex
    In your opinion, what is wrong with this formula? does it do what I am wanting it to do?

    I don't know. I think I don't need the summation symbols. I'm not summing an infinite series for (x,y). I'm just trying to say that if (x,y) is such and such a coordinate, then the line moves from zero as well to the negative of that coordinate.

    I should have waited to post this until I worked with it. Oh well, it was good LaTex practice.

    Again, I realize this takes up your time, so any comments I appreciate.
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  6. #6
    Senior Member yeKciM's Avatar
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    \displaystyle (\forall x,y \in \mathbb{R} ) (y=x)

    it's just a line, and for every x witch goes from \displaystyle -\infty to \displaystyle+\infty u'll have \displaystyle y=x ....
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  7. #7
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    Quote Originally Posted by Flightline View Post
    Thank you, I thought about that, that simply X=Y would do, but that produces an infinite line in both directions. I was looking for a formula, or call it a model, if you will, that indicats that as the line goes to 1,1 it also goes to -1,-1. I
    I'm not certain what you mean by "as the line goes to 1,1 it also goes to -1,-1". A line doesn't "go" to one point or another, it just is there. Perhaps what you mean is a set of functions: f_X(x)= x for -X\le x\le X. Or a function of two variables: f(x,t)= x for -t\le x\le t.
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  8. #8
    Newbie Flightline's Avatar
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    Thanks for the input, and now I wish I had waited before posting about this until I worked it out better. Nevertheless, I know what x = y means, or at least what it looks like. It's a line that runs infinitely in both directions from (0,0), i.e., \{...-3,-2,-1,0,1,2,3...\}

    What I want to show is that there is a force starting at point (0,0). If the force increases in magnitude in one direction, there is a corresponding increase in the other direction. Thus if the increase in magnatude is represented by a line going from (0,0) to (1,1) in the first quadrant of the graph, the line also increases in the third quadrant of the graph from (0,0) to (-1,-1).

    x=y is not the formula that illustrates this, or at least it doesn't seem that way to me. Because as has been pointed out, x=y or other forms of saying the same thing such as \displaystyle (\forall x,y \in \mathbb{R} ) (y=x) merely stand for a line that goes from infinity to infinity along that vector.
    Last edited by Flightline; July 28th 2010 at 08:15 AM.
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  9. #9
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    edit wrong answer
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  10. #10
    Newbie Flightline's Avatar
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    After some more thought, I came up with this. What do you think?

     <br />
\left(f_(_x_)= x | x=n+0)\Longrightarrow \left\left(f_(_x_)= x | x=0-n)

    If y=x such that x = \{1,2,3,...\}; then y=x such that x=\{-1,-2,-3...\}
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  11. #11
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    this is all very confusing. Why are you trying to find an equation to draw 2 vectors at once?

    If your objection to y=x is that it is unbounded, then you can simply add a boundary
    y=x  : -c < x < c

    Alternatively, graph the vectors seperately:
    Vector 1: (c,c)
    Vector 2: -(c,c)
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  12. #12
    Junior Member bondesan's Avatar
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    Flightline,

    Maybe you should see this blog post - the equation of a line segment. I think this is what you're looking for.

    The Equation of a Line Segment

    I hope it helps.
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  13. #13
    Newbie Flightline's Avatar
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    Quote Originally Posted by SpringFan25 View Post
    this is all very confusing. Why are you trying to find an equation to draw 2 vectors at once?

    If your objection to y=x is that it is unbounded, then you can simply add a boundary
    y=x  : -c < x < c

    Alternatively, graph the vectors seperately:
    Vector 1: (c,c)
    Vector 2: -(c,c)
    Thanks, but I don't think that will work for what I'm trying to model. I'm trying to model the idea that as a vector progresses one way, it causes an equal and opposite progression the other way. As to why I'm doing it, well, I'm not sure. I think it represents a concept in a larger concept I'm working on, but since it's probably all a delusion of grandeur anyway, I'd rather not embarrass myself by talking about it.
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  14. #14
    Newbie Flightline's Avatar
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    Quote Originally Posted by bondesan View Post
    Flightline,

    Maybe you should see this blog post - the equation of a line segment. I think this is what you're looking for.

    The Equation of a Line Segment

    I hope it helps.
    I actually think that article will help me a lot in my understanding of what I'm trying to do. Thank you very much for leading me to it. I'm going to give it a good read in the bathtub--the place where all great ideas are born!
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  15. #15
    Junior Member bondesan's Avatar
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    Hahaha, good one. You are welcome.
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