Wow I found a useless equation!!

This is a discussion on Wow I found a useless equation!! within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Here is the equation: Code: high * high - high = low * low + low where high and low ...

  1. #1
    The Defective GRAPE Lurker's Avatar
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    Talking Wow I found a useless equation!!

    Here is the equation:

    Code:
    high * high - high = low * low + low
    where high and low are any real number, and high = low + 1
    I was very bored today, and messed around with my calculator until I found this. Completely uninteresting huh ?
    Do not make direct eye contact with me.

  2. #2
    Senior Member joshdick's Avatar
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    Proof:
    Code:
    Given:  x = y + 1.  Now, prove that x^2 - x = y^2 + y.
    First, square both sides: x^2 = (y + 1)^2
    Expand: x^2 = y^2 + 2y + 1
    Subtract x from both sides: x^2 - x = y^2 + 2y + 1 - x
    We were given that x = y + 1, so substitute on the right side of the equation: x^2 - x = y^2 + 2y + 1 - (y + 1)
    Simplify: x^2 - x = y^2 + y
    Yup
    FAQ

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  3. #3
    The Defective GRAPE Lurker's Avatar
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    Well at least its one of the first equations that wasn't burned to the ground on these forums .
    Do not make direct eye contact with me.

  4. #4
    Senior Member joshdick's Avatar
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    And now because I'm taking a course called Techniques of Math Proof, here's another proof. This one uses case analysis:
    Code:
    x^2 - x ?= y^2 + y
    Factor: x (x - 1) ?= y (y+1)
    Substitute: x (x - 1) ?= xy
    
    Case 1: x != 0
    Divide both sides by x:  x - 1 ?= y
    Add 1 to both sides:  x = y + 1
    
    Case 2:  x = 0
    Given that x = y + 1 and x = 0, y = -1.
    x^2 - x ?= y^2 + y
    Now, just plug in x = 0 and y = -1:
    0 = (-1)^2 + -1
    0 = 1-1
    Yeah, I dig proofs.
    FAQ

    "The computer programmer is a creator of universes for which he alone is responsible. Universes of virtually unlimited complexity can be created in the form of computer programs." -- Joseph Weizenbaum.

    "If you cannot grok the overall structure of a program while taking a shower, you are not ready to code it." -- Richard Pattis.

  5. #5
    Senior Member joshdick's Avatar
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    Originally posted by Lurker
    Well at least its one of the first equations that wasn't burned to the ground on these forums .
    Well, there are now two proofs supporting your conjecture, so one can't argue with the truth. It still remains useless as you said.
    FAQ

    "The computer programmer is a creator of universes for which he alone is responsible. Universes of virtually unlimited complexity can be created in the form of computer programs." -- Joseph Weizenbaum.

    "If you cannot grok the overall structure of a program while taking a shower, you are not ready to code it." -- Richard Pattis.

  6. #6
    C++ Developer XSquared's Avatar
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    For any x, y and a, where they are all elements of R, and y = x - a, x^2 - ax = y^2 + ay.

    Code:
    x^2 - ax = (x - a)^2 + a(x-a)
    x^2 - ax = x^2 - 2ax + a^2 - a^2 + ax
    x^2 - ax = x^2 - ax
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  7. #7
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    a lot of discoveries in the world of mathematics are useless, so don't feel too bad.

  8. #8
    Registered User major_small's Avatar
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    look at it this way: you can use it as a really long way to find out if there are two consecutive numbers... or to prove that high-low=1, if high is low+1 and they're both real numbers
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  9. #9
    The Defective GRAPE Lurker's Avatar
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    Originally posted by major_small
    look at it this way: you can use it as a really long way to find out if there are two consecutive numbers... or to prove that high-low=1, if high is low+1 and they're both real numbers
    Do not make direct eye contact with me.

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