I was presented with a pretty interesting situation the other day:
Can you divide by zero. This is what one physics professor says:
Actually, zero divided by zero is not necessarily infinity. ANY number qualifies as zero divided by zero. It is when you get to dividing NON-zero numbers by zero that you confront infinities.
Think of this in terms of the definition of division. A divided by B means: How many times must you subtract B from A to reach zero?
For A divided by zero, where A is any number except zero, the number is not even infinity, because infinity itself is not big enough. No matter how many times you subtract zero from, say, five, you will never, ever reach zero. So even infinity is not big enough to be 5/0.
What does this tell us about zero divided by zero? Well, how many times must you subtract zero from zero in order to reach zero?
Zero times? Sure. That works.
One time? That works too.
Two times? Yes. If you subtract zero from zero twice, the result is zero.
Pi times? Again, if you subtract pi zeroes from zero, the result is zero.
We can do this with ANY NUMBER THERE IS, even zero. So, zero divided by zero is truly a special way to define a number. The answer can be infinity, or it can be zero, or absolutely anything else. All numbers satisfy the operation.
I want to hear your thoughts and opinions. TheZone -- what say ye?!
Feb 9, 2009 4:19 PM