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Math Help - Division Result

  1. #1
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    Division Result

    What would be the result of the following divisions?

    a. 1/0
    b. 1/INFINITY
    c. INFINITY/0
    d. 0/INFINITY
    e. INFINITY/1
    f. INFINITY/INFINITY
    g. 0/0
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  2. #2
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    depending on what course you are taking, you can use limits to solve most of these, but if not, you simply say they do not exist.

    a. 1/0 Divide by 0, does not exist
    b. 1/INFINITY does not exist
    c. INFINITY/0 divide by 0, does not exist
    d. 0/INFINITY = 0 (0 divided by anything is 0)
    e. INFINITY/1 = INFINITY (dividing in 1 piece is just itself)
    f. INFINITY/INFINITY = 1 (x/x is always 1)
    g. 0/0 = divide by 0, does not exist
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  3. #3
    Junior Member Serena's Girl's Avatar
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    a.) 1/0 = infinity (any positive real number divided by zero is infinity)

    b.) 1/infinity = 0 (any real number divided by infinity is zero)

    c.) infinity/0 = infinity

    say, infinity = r/0, where r = a positive real number
    so... (r/0) / 0 = r / (0*0) = infinity

    d.) 0/infinity = 0

    0 / (r/0) = (0 * 0)/r = 0

    e.) infinity/1 = infinity

    (Divide infinity by any positive number and you obtain infinity. Divide infinity by any negative number and you obtain negative infinity.)

    f.) infinity/infinity = indeterminate

    say, infinity in the numerator = r/0. denominator = s/0, wherein s = a positive real number

    so... (r / 0) / (s / 0) = r/s

    But what is r/s? It can be any rational number. So the answer is indeterminate.

    g.) 0/0 = indeterminate

    say, numerator = r*0, denominator = s*0

    so... (r*0) / (s*0) = r/s

    Again, r/s can be any rational number. Hence, indeterminate.
    Last edited by Serena's Girl; August 6th 2008 at 06:44 PM. Reason: (answers are from a calculus student's point of view)
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  4. #4
    Newbie Coffee Cat's Avatar
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    I saw this site (Math Forum - Ask Dr. Math) just now, and it has an interesting bunch of operations involving infinity and zero.
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  5. #5
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    Wao thanks for the link friend!
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