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Posers and Puzzles

Posers and Puzzles

  1. 19 Sep '07 22:28
    a) x/x is always 1
    b) dividing by 0 is not possible

    What is 0/0? The two rules contadict
  2. Subscriber AThousandYoung
    Proud Boys Beware
    19 Sep '07 22:30 / 1 edit
    Originally posted by The Ewanator
    a) x/x is always 1
    b) dividing by 0 is not possible

    What is 0/0? The two rules contadict
    a) is not correct. You need to have a qualifier so that b) isn't a problem.

    The correct expression is

    x/x = 1, x =/= 0

    x/x is undefined, x = 0
  3. 19 Sep '07 22:32
    OK, cheers, but what would you suggest as an answer to 0/0?
  4. 19 Sep '07 23:40
    Originally posted by The Ewanator
    but what would you suggest as an answer to 0/0?
    If you keep asking questions like this then I'll need to send you to l'Hopital...
  5. 19 Sep '07 23:53
    http://en.wikipedia.org/wiki/Division_by_zero
  6. Standard member EinsteinMind
    Seeker
    20 Sep '07 01:36 / 1 edit
    However, any function where the value x approaches a certain limit and produces a function value 0/0, can be changed or derived to a further to produce a non-zero answer.

    So 0/0 can have some application.

    ex.

    lim (x --> 2) ((x^3)-8)/(x-2) = 0/0

    ((x^3)-8)/(x-2) = (x-2)(x^2+2x+4)/(x-2) = (x^2)+2x+4

    lim (x--> 2) (x^2)+2x+4 = 2^2 + 2(2) + 4 = 12.
  7. Standard member Ramned
    The Rams
    20 Sep '07 01:38
    Originally posted by AThousandYoung
    a) is not correct. You need to have a qualifier so that b) isn't a problem.

    The correct expression is

    x/x = 1, x =/= 0

    x/x is undefined, x = 0
    You're too smart.
  8. 20 Sep '07 01:49
    Originally posted by Diapason
    If you keep asking questions like this then I'll need to send you to l'Hopital...
  9. Subscriber AThousandYoung
    Proud Boys Beware
    20 Sep '07 02:23
    Originally posted by The Ewanator
    OK, cheers, but what would you suggest as an answer to 0/0?
    There is no answer. It's not defined.
  10. Subscriber AThousandYoung
    Proud Boys Beware
    20 Sep '07 02:24
    Originally posted by Ramned
    You're too smart.
    Thanks!
  11. 20 Sep '07 09:11
    How about 0^0?

    x^0 = 1
    0^x = 1

    So what is 0^0?
  12. 20 Sep '07 10:03 / 1 edit
    Rule #1 of math: "You shall not divide by zero!"

    So if you try to divide anything with zero, even zero itself, you violate the rule #1. If you do it anyway you can get any answer, i.e. you cannot ever trust the answer.

    We have a function f(x) = x/x. What is f(0)?
    f(0) = 0/0 = 1 because x/x is always = 1. Right?

    We have another function f(x) = 0/x. What is f(0)?
    f(0) = 0/0 = 0 because 0/x is always = 0. Right?

    So now I have prooved that 0/0 is both =1 and =0. Right?

    Wrong. I divided by zero in both cases, thus violated rule #1, and got a unreliable result. The proofs are worthless.

    Conclusion: Do not ever try to divide by zero!
  13. 20 Sep '07 10:08
    Originally posted by Dejection
    How about 0^0?

    x^0 = 1
    0^x = 1

    So what is 0^0?
    I assume you meant:

    x^0 = 1
    0^x = 0 (or if you like e^x tends to 0 as e tends to 0).

    So what is 0^0.

    The answer is this is actually defined as being equal to 1, mainly so that the binomial theorem works!
  14. 20 Sep '07 12:40
    Originally posted by FabianFnas
    Rule #1 of math: "You shall not divide by zero!"
    It was Rule #7 the way we we're taught
  15. 20 Sep '07 12:50
    Originally posted by mtthw
    It was Rule #7 the way we we're taught
    I would love to see the six first rules of yours!