

Division by zero
Name: chris j stella
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
What happens when you divide a number by 0?
(9/0). Do you get infinity, or just a nullset?
Replies:
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 nullset."
Dr. John
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 Ysequence 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 Nmail (NEWTON mail
as opposed to "email") and we'll work on it.
hawley
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Update: June 2012

