The reason is related to the associated multiplication question. If you
divide 6 by 3 the answer is 2 because 2 times 3 IS 6. If you divide 6 by
zero, then you are asking the question, "What number times zero gives 6?"
The answer to that one, of course, is no number, for we know that zero
times any real number is zero not 6. So we say that division by zero is
undefined, for it is not consistent with division by other numbers.
You can try to make up a good set of rules, but it always leads to nonsense,
so to avoid all the trouble we just say that it doesn't make sense to divide
by zero.
What happens if you add apples to oranges? It just doesn't make sense, so the
easiest thing is just to say that it doesn't make sense, or, as a mathematician
would say, "it is undefined."
Maybe that's the best way to look at it. When, in mathematics, you see a
statement like "operation XYZ is undefined", you should translate it in your
head to "operation XYZ doesn't make sense."
Other details can find in Why can't we divide by zero?
Hope help with this (remember rated this).
Posted on Feb 06, 2010
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Posted on Jan 02, 2017
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