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Francis J. Mueller

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Posted by Tim on November 30, 2003 02:22:18 UTC

author of Elements of Algebra says so.

"Zero divisors are excluded because the resulting quotient would either be contradictory or indeterminant. An example of the first instance might be 7/0. If we represent the quotient as q, then 7/0 = q implies that q*0=7.
But every number, when multipied with 0, has 0 for the product; so 7 as the product for q*0 is impossible. A similar contradiction occurs for every other nonzero dividend and zero divisor.
When both the dividend and the divisor are zero, we have the case of 0/0 . This time let us call the would be quotient k. If 0/0 = k, then k*0=0 which is true for every number in the set that k might represent:
7*0=0, 12*0=0, 1/2*0=0, ect. This implies that 0/0=7, 0/0=12, 1/2/0=1/2 ect. The lack of a unique quotient when the divisor and the dividend are zero makes 0/0 indeterminant.
For these reasons, then, division by zero is excluded."

regards, tim

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