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Posers and Puzzles

Posers and Puzzles

  1. 18 Jan '15 01:09
    Simplify the following exercise in multiplication as much as possible:

    (x+a)(x-b)(x+c)(x-d)...(x-z)

    Please hide your explanation, especially if you have seen the solution.
  2. Standard member Duncan Clarke
    Student
    18 Jan '15 11:57
    0
  3. Standard member wolfgang59
    Infidel
    19 Jan '15 07:38
    Very good. Didn't get it straight away. (Maths degree)
  4. Subscriber sonhouse
    Fast and Curious
    19 Jan '15 18:56 / 2 edits
    Originally posted by wolfgang59
    Very good. Didn't get it straight away. (Maths degree)
    Wouldn't that depend on a multiplication being a zero? I mean, what if X=28 and a=0, b =1, c=2, etc.? Where would there be a zero multiplicand result?
  5. Donation bbarr
    Chief Justice
    19 Jan '15 19:25
    Originally posted by sonhouse
    Wouldn't that depend on a multiplication being a zero? I mean, what if X=28 and a=0, b =1, c=2, etc.? Where would there be a zero multiplicand result?
    One of the items in the series is (x-x)...
  6. Subscriber sonhouse
    Fast and Curious
    20 Jan '15 15:04
    Originally posted by bbarr
    One of the items in the series is (x-x)...
    Yeah, that would do it
  7. 20 Jan '15 23:40
    except if x = +- infinity, when the answer is undefined
  8. Subscriber sonhouse
    Fast and Curious
    21 Jan '15 15:13
    Originally posted by iamatiger
    except if x = +- infinity, when the answer is undefined
    Is infinity minus infinity undefined?
  9. 21 Jan '15 19:22
    Originally posted by iamatiger
    except if x = +- infinity, when the answer is undefined
    as x --> infinity, x - x = what?
  10. Subscriber Ponderable
    chemist
    21 Jan '15 19:32
    Originally posted by iamatiger
    except if x = +- infinity, when the answer is undefined
    infinity is a symbol not a number, so x can't equal infinity...Even the lim(x->infinity) doesn't yield any kind of problem.
  11. 23 Jan '15 00:34 / 3 edits
    Infinity - Infinity is undefined, as with an infinite number of hotel rooms I can either put an infinite number of guests in every room, having zero free rooms, or I can put an infinite number of guests in every second room, having an infinite number of free rooms, or I can miss out any finite number of rooms at the start, and still fit my guests in with that finite number of rooms left.

    I think claiming infinity is a symbol and not a number is rather dodgy. All numbers are symbols too, and infinity comes up in valid mathematics. If you are worried about saying x=infinity, then let us define x=1/0
  12. 23 Jan '15 01:00 / 2 edits
    Originally posted by iamatiger
    Infinity - Infinity is undefined, as with an infinite number of hotel rooms I can either put an infinite number of guests in every room, having zero free rooms, or I can put an infinite number of guests in every second room, having an infinite number of free rooms, or I can miss out any finite number of rooms at the start, and still fit my guests in with t ...[text shortened]... es up in valid mathematics. If you are worried about saying x=infinity, then let us define x=1/0
    So pretending, we have x = 1/0.

    What is 1/0 - 1/0?

    Multiply both sides by 0. Eliminates the 0's.

    We have 1-1.*

    What is 1-1?

    0.

    Ergo, x-x=0 even when x=1/0 in the pretend world.

    *Edit: or we have 0-0 at the starred equation. Same outcome.
  13. 24 Jan '15 08:58

    multiplying both sides by 0 just proves 0=0 (as 0 converts everything to 0)

    4 = 5
    multiply both sides by 0
    0 = 0

    0/0 is undefined too, by the way
  14. Standard member wolfgang59
    Infidel
    31 Jan '15 04:24
    Originally posted by iamatiger
    except if x = +- infinity, when the answer is undefined
    x-y may be undefined where both x and y ->inf but x-x ???

    It is zero, even when x->inf