Division by zero
Name: chris j stella
What happens when you divide a number by 0?
(9/0). Do you get infinity, or just a null-set?
If you are talking about division in the real numbers, then the answer is
that values of expressions of the form x/0 are undefined. In other words,
you don't "get" anything because the expression cannot be evaluated.
Perhaps that is what you mean by getting "a null-set."
Dr. John is absolutely correct: the definition of division on the
Reals does not allow division by zero; however...
it's perfectly alright to ask what is X/Y as Y *approaches* zero.
Mathematically, we use the expression: lim(Y --> 0) X/Y,
where the "Y --> 0" is usually written just below the "lim" word.
And the answer is +/- INF (plus or minus infinity) depending on the
signs of X and Y. For example, suppose X=1 (it could be any Real constant)
and we evaluate X/Y for different values of Y as Y gets smaller and
smaller, approahing zero, like in the sequence 1, 1/2, 1/3, 1/4, ...
(the three dots are called "elipses" and mean that the sequence continues
forever). Then X/Y forms the sequence 1, 2, 3, 4, ...
and you can see that the LIMIT of the Y-sequence approaches zero and the
limit of the X/Y sequence just keeps on getting larger and larger, and we
say that the limit of X/Y approaches infinity.
There's a subtle but very important distinction here between:
1) setting Y equal to zero and
2) letting Y approach zero
I hope it's not too confusing; if it is, send me N-mail (NEWTON mail
as opposed to "e-mail") and we'll work on it.
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Update: June 2012