Re: What is zero divided by zero anyway?

I have always thought that there are three possible answers to the question what is 0 / 0:

zero, since zero divided by anything is still zero;
infinity, since anything divided by zero is infinity;
one, since anything divided by itself is one.

Of course my thinking can be very wrong as zero is not just anything -- it is a special case in itself. 0 / 0 may be equal to zero, one and infinity at the same time, but it is probably easier to say that it is undefined. Or even Mu.

Comment on Re: What is zero divided by zero anyway?

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Re^2: What is zero divided by zero anyway? by Aristotle (Chancellor) on Oct 06, 2002 at 10:39 UTC
Yes, the answer is that the result of x/0 (including x=0) is every possible result at once. That is because x0 is zero for any x. With xa for any a != 0 the result set is exactly as large as the definition set (I hope these are the correct English terms). But for a = 0, the result set has only a single value, 0 itself. xa maps every x to one distinct y, except for a=0, so you can reverse it. But for a=0, it maps every x to the same y (that is, to 0), so by knowing a=0 and y=0 you still cannot tell which out of an infinite number of possible values for x led to this result. Makeshifts last the longest.*	[reply]

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Re^2: What is zero divided by zero anyway?
by Aristotle (Chancellor) on Oct 06, 2002 at 10:39 UTC

Yes, the answer is that the result of x/0 (including x=0) is every possible result at once. That is because x*0 is zero for any x. With x*a for any a != 0 the result set is exactly as large as the definition set (I hope these are the correct English terms). But for a = 0, the result set has only a single value, 0 itself.

x*a maps every x to one distinct y, except for a=0, so you can reverse it. But for a=0, it maps every x to the same y (that is, to 0), so by knowing a=0 and y=0 you still cannot tell which out of an infinite number of possible values for x led to this result.

Makeshifts last the longest.

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