2 = 1 NOT

Discussion in 'Miscellaneous' started by XxBoWnZxX666, Mar 7, 2012.

  1. The following example uses division by zero to "prove" that 2 = 1, but can be modified to prove that any number equals any other number.
    1. Let a and b be equal non-zero quantities
    A = B
    2. Multiply through by a
    A² = AB
    3. Subtract
    A² - B²
    4. Factor both sides
    (A - B)(A + B) = B(A - B)
    5. Divide out (A - B)
    A + B = B
    6. Observing that
    B + B = B
    7. Combine like terms on the left
    2B = B
    8. Divide by the non-zero b
    2 = 1

    The fallacy is in line 5: the progression from line 4 to line 5 involves division by a − b, which is zero since a equals b. Since division by zero is undefined, the argument is invalid. Deriving that the only possible solution for lines 5, 6, and 7, namely that a = b = 0, this flaw is evident again in line 7, where one must divide by b (0) in order to produce the fallacy (not to mention that the only possible solution denies the original premise that a and b are nonzero). A similar invalid proof would be to say that since 2 × 0 = 1 × 0 (which is true), one can divide by zero to obtain 2 = 1. An obvious modification "proves" that any two real numbers are equal.

    Many variants of this fallacy exist. For instance, it is possible to attempt to "repair" the proof by supposing that a and b have a definite nonzero value to begin with, for instance, at the outset one can suppose that a and b are both equal to one:

    A = B = 1

    However, as already noted the step in line 5, when the equation is divided by a − b, is still division by zero. As division by zero is undefined, the argument is invalid.
    Monster_ likes this.
  2. Haha Nice Twitch, and Jeremy, your thing didn't work?
  3. Huh?
  4. math is some pretty cool stuff to be honest. have you ever seen minute physics on youtube? his videos are great!
  5. EDIT: I tried to say that the fail is at line 3, not line 5.
    So basically A²=AB --> A²-B² ????
    I got lost, how in hell Apples² = Apples(pears) becomes Apples²-Pears² ?????
    the correct way to solve A²=AB would be in case A²/AB=0 which actually is A/B=0
    I believe your above statment it's kinda weird :p
    Monster_ likes this.
  6. i concur.
  7. Thats what happend to me when I read this! Lol
    Monster_ likes this.
  8. From the GIF you posted here:
    "this image can't be displayed for the momment, please go to www.example.com to see it."
  9. There is just the weirdest links ever on it!@!
  10. Changed it :p
  11. However, AB/AB = 1. Your statement is kinda weird :p
  12. Still the same... lol
  13. A²=AB will never be AB=AB
    Not in real/normal math.
    Maybe: A²/A=B which could be:
    But that brings you back to the start :p
  14. Fixed I think, lol
  15. L-O-L.
  16. Oh god....Thats gonna give me nightmares :(
  17. Well, if A2 = AB, then we can simplify in the following steps:
    A2 / AB = AB/AB
    Therefore A2 / AB = 1.
  18. Which will then lead you back to the first equation, A = B.
    But copherfield has a point. I also don't understand step 2 ~ 3.

    A² = AB
    Subtract A² - B² From A² = AB.
    It'll give you
    -B² = A² - B² + AB, then
    0 = A² + AB, then
    0 = A(A +B),