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  1. #1
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    "proofs" that 1=0 (fallacious of course)

    I used to have three fallacious proofs that 1=0.

    The first one was regarding infinite series:

    0 = (1-1) + (1-1) + ...
    = 1 + (-1 + 1) + (-1 + 1) + ...
    ergo, 0=1

    The second one was based on dividing by zero:

    0 x 0 = 0
    0 x 1 = 0

    0 x 0 = 0 x 1

    divide both sides by zero
    0/0 x 0 = 0/0 x 1
    ergo 0=1


    The last one, I forgot, it was integral based. Anyone have any ideas which it was?

  2. #2
    riding once again jschen's Avatar
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    Let's be a bit more subtle.

    a = b
    a^2 = a * b
    a^2 - b^2 = a * b - b^2
    (a + b) (a - b) = b (a - b)
    a + b = b

    since a = b...

    2b = b
    2 = 1

    2 - 1 = 1 - 1
    1 = 0

    Yes... it's still a division by zero fallacy, but at least we don't outright show a big fat 0 in the denominator.
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  3. #3
    On my TARDIScycle! KingTermite's Avatar
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    Quote Originally Posted by jschen View Post
    Let's be a bit more subtle.

    a = b
    a^2 = a * b
    a^2 - b^2 = a * b - b^2
    (a + b) (a - b) = b (a - b)
    a + b = b

    since a = b...

    2b = b
    2 = 1

    2 - 1 = 1 - 1
    1 = 0

    Yes... it's still a division by zero fallacy, but at least we don't outright show a big fat 0 in the denominator.
    At least this version followed math rules and could be followed.


    The ones in O.P. just took leaps with no math rules being followed....it made no sense.
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    - it's pretty well established that Hitler was an *******.

  4. #4
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    I think he was trying to use the propery of one.

    Anything/itself=1 (except 0)

    5/5=1, 1/1=1, but the exception 0/0=0 still, unless I'm remembering math all wrong.
    Quote Originally Posted by mlts22 View Post
    I used to have three fallacious proofs that 1=0.

    The first one was regarding infinite series:

    0 = (1-1) + (1-1) + ...
    = 1 + (-1 + 1) + (-1 + 1) + ...
    ergo, 0=1

    The second one was based on dividing by zero:

    0 x 0 = 0
    0 x 1 = 0

    0 x 0 = 0 x 1

    divide both sides by zero
    0/0 x 0 = 0/0 x 1
    ergo 0=1


    The last one, I forgot, it was integral based. Anyone have any ideas which it was?
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


    . “He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.”- Fredrick Nietzsche

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  5. #5
    Jewish Media Conspirator asherlighn's Avatar
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    Quote Originally Posted by Tom Stormcrowe View Post
    I think he was trying to use the propery of one.

    Anything/itself=1 (except 0)

    5/5=1, 1/1=1, but the exception 0/0=0 still, unless I'm remembering math all wrong.
    You are remembering math correctly. It is deliberately wrong. Designed to make students look at the intermediary steps in proofs (atleast thats where I first saw it).
    Quote Originally Posted by dutret
    The fact is that most peoples sense of what rides well is easily overcome by their sense of what looks cool.

  6. #6
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    Quote Originally Posted by asherlighn View Post
    You are remembering math correctly. It is deliberately wrong. Designed to make students look at the intermediary steps in proofs (atleast thats where I first saw it).
    Come to think about it, the result would either be 0 or undefined, depending on the application!
    If it's a slope, the result would be undefined.
    y=mx+b, with y=o and x=0, it would be an undefined result(vertical line right on the y axis, through the 0,0 intersection or origin)
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


    . “He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.”- Fredrick Nietzsche

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  7. #7
    Displaced Southerner polara426sh's Avatar
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    Quote Originally Posted by Tom Stormcrowe View Post
    Come to think about it, the result would either be 0 or undefined, depending on the application!
    If it's a slope, the result would be undefined.
    y=mx+b, with y=o and x=0, it would be an undefined result(vertical line right on the y axis, through the 0,0 intersection or origin)
    Or it could be a line to another dimension. One where the narrator is Rod Serling.

  8. #8
    Air
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    Destroyer of Wheels Air's Avatar
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    Quote Originally Posted by mlts22 View Post
    I used to have three fallacious proofs that 1=0.

    The first one was regarding infinite series:

    0 = (1-1) + (1-1) + ...
    = 1 + (-1 + 1) + (-1 + 1) + ...
    ergo, 0=1
    Actually, if you continued this out it would actually be:

    0 = 1 + (-1 + 1) + (-1 + 1) + ... + -1 + ....

    0 = 1 - 1 = 0
    Last edited by Air; 07-25-07 at 01:02 PM.

  9. #9
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    Quote Originally Posted by polara426sh View Post
    Or it could be a line to another dimension. One where the narrator is Rod Serling.
    Nope, because for that to occur, you'd have to factor in the tau axis and teh axis if you want to include multiverse theory, as well as x,y, and z on multiple axis', thereby winding up with something more like 0/∞, or ∞/0.
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


    . “He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.”- Fredrick Nietzsche

    "We can judge the heart of a man by his treatment of animals." - Immanuel Kant

  10. #10
    Crawlin' up, flyin' down bikingshearer's Avatar
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    Quote Originally Posted by Tom Stormcrowe View Post
    I think he was trying to use the propery of one.

    Anything/itself=1 (except 0)

    5/5=1, 1/1=1, but the exception 0/0=0 still, unless I'm remembering math all wrong.
    Maybe I'm remembering math all wrong (highly likely; if I could do math or science, I wouldn't be a lawyer ) but isn't dividing by zero impossible regardless of what number you are dividing?
    "I'm in shape -- round is a shape." Andy Rooney

  11. #11
    DocRay
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    Quote Originally Posted by jschen View Post
    Let's be a bit more subtle.

    a = b
    a^2 = a * b
    a^2 - b^2 = a * b - b^2
    (a + b) (a - b) = b (a - b)
    a + b = b

    since a = b...

    2b = b
    2 = 1

    2 - 1 = 1 - 1
    1 = 0

    Yes... it's still a division by zero fallacy, but at least we don't outright show a big fat 0 in the denominator.
    Yep. This proves it, computer's can't work.

  12. #12
    Banned. red house's Avatar
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    Quote Originally Posted by bikingshearer View Post
    Maybe I'm remembering math all wrong (highly likely; if I could do math or science, I wouldn't be a lawyer ) but isn't dividing by zero impossible regardless of what number you are dividing?


    Yep.. looks like he forgot to use L'Hôpital's Rule.

  13. #13
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    Quote Originally Posted by bikingshearer View Post
    Maybe I'm remembering math all wrong (highly likely; if I could do math or science, I wouldn't be a lawyer ) but isn't dividing by zero impossible regardless of what number you are dividing?
    It's conceptualized as "Undefined", actually.
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


    . “He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.”- Fredrick Nietzsche

    "We can judge the heart of a man by his treatment of animals." - Immanuel Kant

  14. #14
    Crawlin' up, flyin' down bikingshearer's Avatar
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    Quote Originally Posted by Tom Stormcrowe View Post
    It's conceptualized as "Undefined", actually.
    Ahhhhh, got it. Sort of like a lawyer's soul.
    "I'm in shape -- round is a shape." Andy Rooney

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