 # Dividing by Zero

That has never been the way that I have heard mathematicians define infinity. Infinity isn’t a defined, if unknown, quantity; infinity is, by definition, larger than any number. Doesn’t matter how big a number you come up with - a googol? Infinity is bigger, because infinity is infinite. Therefore, the operations performed on infinity don’t matter. You multiply an infinite set of things by two, and you still have an infinite set of things. Infinity times two is still infinity.

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No, you have the the value of infinity + the value of infinity.

And by undetermined I mean that the value cannot be written or shown fully. Such as i, pi, or e. The only thing that these have that infinity doesn’t is that these values, with the exception of i, which is an exception, is that we know what these numbers start with, and can use parts of it in calculations. With infinity that isn’t possible.

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Infinity doesn’t have a value to be written, fully or not. It is a concept or a value greater than any number. π and e are simply irrational numbers; by their definition, they have a defined value, but the decimals don’t repeat so we can never write them in their exact form and need to approximate when using them. i is an imaginary number, defined as sqrt(-1) and having no integer or decimal approximation itself. Infinity is none of these things, add you correctly identified. We have no value for it because there is no value to be ascribed to it. Any number you can try and use, there is a number higher than it, so that number is not infinity. Infinity is a value greater than any assignable quantity or countable system. By definition, you cannot have two of those.

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True, but infinity DOES have a value. It’s value is infinite.

Okay, let me take a step back here, and explain my reasoning here.

Let’s step back from multiplication, which would be adding infinity multiple times, and do just addition.

Let’s add something simple, like, ∞+4.

At first glance, one would think, “oh, infinity plus four, because infinity is infinite, it has all values, so the answer must be infinity? right?”

Wrong. It’s ∞+ 4, and here’s why.

No matter what value you pick for infinity, the answer will always be, 4 more than that. The answer is not infinity, it’s 4 more than infinity.

Now, let’s step up to multiplication.

2x∞.

Multiplication, is simply just one number, added the amount of times of the other number. I could take the hard route and do infinite 2’s, but I’ll take the easy route here.

2x∞ = ∞+∞

Now, we’re in the same situation as the first question. The answer is not infinity, it’s infinitely more than infinity. Obviously, this can’t be written, so we leave it as ∞+∞, or 2x∞.

All you can do to reduce this is divide it by 2, or by ∞.

Now, powers.

∞^2.

Now, powers are just multiplication over and over, correct? So,

∞^2 = ∞x∞

Now, we have infinity multiplied infinite times, which can’t be written, so we leave it as ∞x∞ or ∞^2.

In conclusion, what I’m trying to say is, infinity is an incombineable term, just like variables.

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Not quite. You seem to be hung up on the notion of “picking a value for infinity.” Infinity, by definition, doesn’t have a set value. So “infinity + 4” isn’t “a large number we don’t know + 4”, it’s “the concept of an uncountable, unending number + 4”. Having four greater than the concept of an uncountable, unending number is, still, the concept of an uncountable unending number. That’s just how the concept of an uncountable, unending number works.

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And therefor, that IS it’s value, the endless, uncountable number. So that IS the value you pick for infinity, and now (using the example I gave) it’s endless, uncountable number, +4.

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There are different ways of looking at infinity, but in all of them, its existence is valueless. 2 X Infinity is the same things as Infinity.

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The thing is that pizzas cannot just become infinite in real life. As I said at the begining math exists to serve real life and its problems. Math has to follow the laws of the world so pizza cannot become infinite because you divide it zero times.

Undefined is a real world answer

That fact sorta undermines your argument

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If you divide something by zero, you are dividing it by nothing, you’re dividing it no times.

so if you have a slice of pizza and divide it no times, it is one slice of pizza.
if you divide the slice of pizza by one, you still get one slice of pizza.

if you divide 2 by 0, you still have 2 because you technically didn’t divide it.
If you divide 2 by 1, you get two because that’s just how the math works.

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It is absolutely not an answer in this situation. If I divide a pizza zero times the pizza doesn’t become undefined. It’s clearly still a pizza

Finally someone gets it.

Dividing by nothing isn’t the same as not dividing

When you have an operation of division you have to do something. In this case it’s dividing by zero, which has previously been stated to be impossible and all by people much more knowledgable than I

Yeah, you have a pizza, but you’re unable to divide it because what you would need to divide it into is an undefined value

It still applies to real world situations

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You’re not dividing it into zero, you’re dividing by zero. Obviously an object cannot simply disappear or become undefined in real life. If I divide a pizza zero times the pizza remains in its original form. Also zero is not an undefined value it’s zero, the lack of numbers.

Correct

Incorrect

Something doesn’t become “undefined“ because undefined isn’t an answer that can be found. The point of an undefined value is that you are unable to find it. If you try to divide a pizza by zero you don’t get the whole pizza as an answer, you get something that can not be found as an answer

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If you cut a pizza zero times the pizza remains in its original form. The answer is simple.

Here’s another analogy my friend came up with to try and prove me wrong. If you have ten apples and you divide it into five piles you have divided by five. If you divide ten apples into zero piles it doesn’t make sense. What I said in response was that if you divide the apples into zero piles then that means you left them as they were in one pile together. There was one pile even though I didn’t divide them.

That’s by dividing by 1. If you divide one pizza out of one piece of pizza you keep the one pizza untouched. If you divide one pizza into zero pieces of pizza you see it is quite impossible

Now for the apple analogy, the issue you are having here is that you’re not realizing that you are leaving the apples untouched because it is impossible to do what dividing by zero requires. You can not find the undefined value and so you can’t complete the operation of dividing by zero.

Your friend is right and I recommend you listen to him

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Dividing into zero piles isn’t the same as dividing into one pile - you as much as say that yourself.

Really, though, I’m questioning what you expected when you made this topic. You’re trying to claim that hundreds of years of mathematicians, the vast majority of whom are smarter than myself and likely you (though I don’t mean to presume), are wrong because, by your reckoning, dividing something by zero is the same as dividing by one. Now that’s fine in its own right, discussion and debate are good ways to deepen our understanding of complex and abstract topics such as math, but you started the topic, before even explaining your own perspective, by telling people to not even mention the current consensus. If you don’t want people to discuss or explain the agreed upon answer, then what discussion were you planning to incite? Why start a discussion by telling people not to disagree with you?

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Yes but you can’t divide an object by zero in real life so it cannot be expressed in these terms.

Also @ProfSrlojohn your arguments for infinity are correct if the terms of the equation are in infinity, if not then those rules don’t apply necessarily. Maths is fun.

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Yeah. I think better in equations than in proofs.

Which is why I didn’t do that well in geometry.

Pre-cal was fun though.

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I saying that you have 1 whole pizza and that to divide by zero is the same as asking how many slices of no pizza can fit inside a whole pizza? There’s no way to answer the question. 1 pizza divided by 0 pizza = ??? You’re trying to answer how much of nothing can fit into something. It can’t be answered.