Why divided by 0 is undefined

Ask for example what we obtain when adding a number to infinity. The common perception is that infinity plus any number is still infinity. If that's so, then. That in turn would imply that all integers are equal, for example, and our whole number system would collapse.

So, in that case , what does it mean to divide by zero? That's OK as far as it goes, any number z satisfies that equation. We could argue that it's 1, or 2, and again we have a contradiction since 1 does not equal 2. This is a millionth. So we see a pattern here. As we divide one by smaller and smaller and smaller positive numbers, we get a larger and larger and larger value.

Based on just this you might say, well, hey, I've got somewhat of a definition for 1 divided by 0. Maybe we can say that 1 divided by 0 is positive infinity. As we get smaller and smaller positive numbers here, we get super super large numbers right over here.

But then, your friend might say, well, that worked when we divided by positive numbers close to zero but what happens when we divide by negative numbers close to zero? So lets try those out. Well, 1 divided by negative 0. And, if we go all the way to 1 divided by negative 0. So you when we keep dividing 1 by negative numbers that are closer and closer and closer and closer to zero, we get a very different answer.

We actually start approaching negative infinity. So over here we said maybe it would be positive infinity, but you can make an equally strong argument that it could be a very different number.

Because zero is neither positive nor negative, the term nonnegative is sometimes used to refer to a number that is either positive or zero, while nonpositive is used to refer to a number that is either negative or zero.

Zero is a neutral number. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1. The rule is that any number raised to the power of 0 equals to 1. So if 2 or 1,, is raised to the power of 0 it equals 1. Begin typing your search term above and press enter to search.

Press ESC to cancel. Skip to content Home Is 0 divided by a number undefined? Now, this got me thinking about basic arithmetic and how to prove each operation, and I created a mental inconsistency between multiplication and division.

As this is an important part of the thought process that lead me down this mental rabbit hole, I am including the elementary explanation of multiplication. Let's say that I am a wandering saint and I have 50 apples. I want to help the hungry people of the world so I give my apples away freely. Now, let's handle two similar scenarios. But it has me thinking, if I divide a pizza into zero equal slices, well then I essentially didn't slice the pizza and thus still just have an entire pizza.

How can it be proved thoroughly, not just with math, but with an example explanation understandable by children that division by zero is truly undefined?

That division by zero is undefined cannot be proven without math, because it is a mathematical statement. It's like asking "How can you prove that pass interference is a foul without reference to sports? So we can can a class of objects in which we call one of the objects "zero", and have a class method such that "division" by "zero" is defined, but that class will not act exactly like the real numbers do. Another definition of division is in terms of repeated subtraction.

If you take 50 apples and give one apple each to 10 people, then keep doing that until you run out of apples, each person will end up with 5 apples. You're repeatedly subtracting 10 from 50, and you can do that 5 times.

If you try to subtract 0 from 50 until you run out of apples, you'll be doing it an infinite number of times. The answer is clearly no because any number times zero always gives you zero. We know that any number times zero is zero.

This kind of division problem gives you an infinite number of answers instead of just one as it should be. Here's another very simple example for good measure.

How much pizza will each person get? Well, you have no people to give the pizzas to. Practically speaking, this is unanswerable.