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Explaining the impossibility of dividing by zero

Discussion in 'Mathematics' started by AVDBA, Sep 19, 2019.

  1. AVDBA

    AVDBA New commenter

    Frequently, one encounters an argument for explaining to students that a division by zero is not allowed by means of leading to infinite result. The following route is interesting, since it leads to a logical flaw.

    Suppose that:

    x = y

    hence:

    xy = x^2

    Now, by subtracting y^2, one reaches:

    xy - y^2 = x^2 - y^2

    and, by factoring:

    y(x - y) = (x + y)(x - y)

    Now, dividing by (x - y), one obtains:

    y = x + y

    But, x = y, hence:

    y = 2y

    meaning that:

    1 = 2

    i.e., an absurd.
     

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