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When we use math, we usually use it in one of two ways: tangible and intangible methods. This kind of question asks us to negate everything we have been taught, ever proved to be logically true, and ask that big "What if" question. Since math does explain that which cannot be seen, we can actually look at this from a different perspective.

Math allows us to identify quantities with labels. This is shown with the letter "i", which is the square root of -1. Now "i" is an intangible entity, but it can be used tangibly in problems. Can we actually take the square root of -1?

It's the same type of question! But since it comes up so much, mathematicians realized it can't be zero, it can't be infinity, and who knows what it really is. Rafaello Bombelli called it an imaginary number, and named it i. So why can't we do the same for division by zero?

Suppose we give division by zero, ie 1/0, an appropriate label, Ze. Further, lets pick an arbitrary problem, something relatively simple, A series: 1/0, 2/0, 3/0....infinity/0.

Now lets represent that series with the new term, Ze:

nZe where n=1 to infinity

So - what does that tell us? Well, it tells me that I either earned my Applied Math and Statistics Degree or I'm channeling Leibniz (and not by choice, mind you). Because it's just a polite way of representing division with zero! It doesn't say whether I can do it or not, but it doesn't just shut the problem down either. It leaves open the possibility of division by zero.

Now - lets get off the paper reality for a moment and think about the logic of division by zero. Division by zero means dividing something by essentially an entity that we consider to be, nothing. Not 1, which results in the same entity, but NOTHING! Multiplication by nothing results in nothing by our current rules. And why is that? Lets take a look:

If we were to do a simple multiplication like 2 x 3, we get this:

2 x 3 = 2 + 2 + 2 = 6 add 2 three times: this is simple math

But what if we had 2 x 0?

2 + ? well add 2 zero times. huh?

What really happens here? How do we explain that 2 x 0 = 0? Can we say, 2 collapses into itself because you can't multiply something by 'nothing' times? In the other example you simply add the first number by itself, the amount of times being determined by the second term. That's easy enough. But if the second number is zero? Houston, we have a minor problem!

Never fear - we can use one of our trusty rules (Associative property for multiplication) and turn it around:

2 x 0 = 0 x 2 Aha!

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