Results 1 to 15 of 15

Math Help - Odd proof - Can you spot the error?

  1. #1
    Junior Member SuperCalculus's Avatar
    Joined
    Feb 2010
    Posts
    34

    Odd proof - Can you spot the error?

    Let a = b.

    Hence, a^2 = ab.

    So, 2a^2-2ab = a^2 - ab

    2(a^2-ab) = 1(a^2-ab)

    Hence, 2=1?!
    I showed this to two maths teachers at my school who couldn't figure this... Let's see how you guys fare.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    The reason 2(a^2 - ab) = a^2 - ab is because a^2 - ab = 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member SuperCalculus's Avatar
    Joined
    Feb 2010
    Posts
    34
    Quote Originally Posted by icemanfan View Post
    The reason 2(a^2 - ab) = a^2 - ab is because a^2 - ab = 0.
    Indeed, this is correct. Nice one.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    Quote Originally Posted by SuperCalculus View Post
    Indeed, this is correct. Nice one.
    Thanks. For the record, I have never seen that "proof" before.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,234
    Thanks
    27
    Quote Originally Posted by SuperCalculus View Post

    2(a^2-ab) = 1(a^2-ab)

    Hence, 2=1?!
    You have divided by 0, which is impossible to do.

    a = b \implies a-b=0

    Also check your steps, the hole thing seems poorly constructed.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,234
    Thanks
    27
    Quote Originally Posted by icemanfan View Post
    Thanks. For the record, I have never seen that "proof" before.
    I have seen ti many times, it goes like this

    a =b

    a^2 = ab

    a^2-b^2 = ab-b^2

    (a-b)(a+b) = b(a-b)

    Zero division here

    a+b = b

    b+b = b

    2b = b

    2=1
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by SuperCalculus View Post
    Let a = b.

    Hence, a^2 = ab.

    So, 2a^2-2ab = a^2 - ab

    2(a^2-ab) = 1(a^2-ab)

    Hence, 2=1?!
    I showed this to two maths teachers at my school who couldn't figure this... Let's see how you guys fare.
    honest ?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member SuperCalculus's Avatar
    Joined
    Feb 2010
    Posts
    34
    Quote Originally Posted by Archie Meade View Post
    honest ?
    Seriously. Shocking, isn't it?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member Aryth's Avatar
    Joined
    Feb 2007
    From
    USA
    Posts
    651
    Thanks
    1
    Awards
    1
    Quote Originally Posted by SuperCalculus View Post
    Seriously. Shocking, isn't it?
    Wow...

    Just wow...
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member integral's Avatar
    Joined
    Dec 2009
    From
    Arkansas
    Posts
    200
    It is not surprising. I have come to learn over the years, high school teachers are mostly idiots who only know what the school expects them to teach. Which is not much
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    This one can be found on Wikipedia if my memory is correct. It is indeed a division by zero.

    high school teachers are mostly idiots who only know what the school expects them to teach.
    Indeed. I had a high school teacher. I was interested in his knowledge. I asked him something a bit advanced (modular arithmetic). He looked at me, blinked, and told me to finish my worksheet. Lame. I don't recall having any math teacher that actually was interested in maths.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by Bacterius View Post
    This one can be found on Wikipedia if my memory is correct. It is indeed a division by zero.


    Indeed. I had a high school teacher. I was interested in his knowledge. I asked him something a bit advanced (modular arithmetic). He looked at me, blinked, and told me to finish my worksheet. Lame. I don't recall having any math teacher that actually was interested in maths.
    Haha. This reminds me of my high school teacher who did not know the spelling of Epsilon! And he had a MS in Physics!
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Bacterius View Post
    This one can be found on Wikipedia if my memory is correct. It is indeed a division by zero.


    Indeed. I had a high school teacher. I was interested in his knowledge. I asked him something a bit advanced (modular arithmetic). He looked at me, blinked, and told me to finish my worksheet. Lame. I don't recall having any math teacher that actually was interested in maths.
    My High school teach Mr. Pillion is the one that kindled my love for math. He may not have been a theoretician but his love for Calculus was all it took.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Quote Originally Posted by Drexel28 View Post
    My High school teach Mr. Pillion is the one that kindled my love for math. He may not have been a theoretician but his love for Calculus was all it took.
    Aww, teaching is so much more, so much more effective when the teacher enjoys what he's talking about, it really gives a different feel to the lesson (as I experienced it in biology). Sadly this world is not about a better education but about higher profit (high school teachers are cheap to manufacture)
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Newbie
    Joined
    Mar 2010
    Posts
    9
    Ignoring the last equation and simplifying the second to last one, I got 2A^2-2A^2=A^2-A^2, which is of course 0=0.

    I know it's late, but I didn't look at all your guys' answers and solved it on my own, and wanted to check if my solution was correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Spot my mistake please...
    Posted in the Statistics Forum
    Replies: 4
    Last Post: September 8th 2010, 03:15 AM
  2. Can anyone spot my error?
    Posted in the Math Software Forum
    Replies: 3
    Last Post: February 4th 2010, 07:49 PM
  3. How do you spot it's a substitution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 17th 2009, 07:17 AM
  4. Mean square error proof
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 23rd 2009, 05:51 PM
  5. Spot the formula
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 25th 2008, 08:54 PM

Search Tags


/mathhelpforum @mathhelpforum