Example I have a pizza I cut it into zero pieces shouldnt it be still one whole pizza?
Since I didn’t cut it so it’s still whole
In: 0
Let’s say the pizza is laying on a table and meant to feed x amount of people. If there’s one person he gets everything. If there are two, both get half of it and so on. If nobody occures the whole idea the pizza feeds people makes no sense – undefined.
So dividing by zero Being NaN for your example is not that you are cutting a pizza zero times(which is why any 0/1 = 0 meaning you cut it 0 times) you have zero pizzas and you need to cut it at least 1 time. You can’t cause you got no pizza to cut
Think about it.
10/5.
It means, basically, “take ten identical pieces, divide equally into five piles”.
So. 10/0 then. “Take ten identical pieces, divide equally into ZERO piles.”
That…that is impossible, if you boil it down. There can be no answer to that, because you cannot do it. You cannot expect an answer on something you are unable to do.
This is a way to produce infinite number of pizzas. If you cut it into 0.5 pieces you will get 2 pizzas. If you cut it into 0.25 pieces you will get 4 pizzas. If you follow that logic, cutting pizza into 0 pieces should give you infinite number of pizzas. At least this is a limit of 1/x when x->0
Unfortunately cutting pizza is defined only on natural numbers.
If you cut a pizza into 2 pieces, how many of those pieces would you need to put together to make a whole pizza? Two, right?
If you cut a pizza into 3 pieces, how many of those pieces would you need to put together to make a whole pizza? Three right?
If you cut a pizza into “0” pieces, how many of those pieces would you need to put together to make a whole pizza? Er…
Division by zero is undefined because it’s meaningless and people get confused when you “cut something into 0 pieces” (which is not the same as “don’t cut the pizza”, as the trap you fell into… that’s actually just “cutting it into 1 piece”, i.e. leaving it intact).
All you have to do is look at it the other way around.
12 / 4. How many 4’s do you need to add together to make 12? 3 of them. 4 + 4 + 4
12 / 2. How many 2’s do you need to add together to make 12? 6 of them. 2 + 2 + 2 + 2 + 2 + 2
12 / 0. How many 0’s do you need to add together to make 12?
Try it. 0. +0. +0. +0. Still adding up to zero. Should we keep going? +0 +0 +0 ? When will we hit 12? Never.
And even if you consider the SINGLE exception:
0 / 0. How many 0’s do you need to add together to make 0? Well, one. One zero added together will total zero. But so will two zeroes. And three zeroes. In fact any number of zeroes, added together, will total 0.
So the “answer” is either: No amount of 0’s will add up to the target number. Or EVERY amount of zeroes will add up to the target number.
Hence, division by zero is just unnecessarily difficult, complicated, fairly useless, and doesn’t help, and thus is generally undefined.
> Example I have a pizza I cut it into zero pieces shouldnt it be still one whole pizza? Since I didn’t cut it so it’s still whole
You’re confusing the number of times you “cut” the pizza with the number you split into.
If you want to split the pizza into 3 pieces, you have to cut it 2 times. That is division by 3.
If you split the pizza into 2 pieces, you have to cut it 1 times That is division by 2.
If you want to split the pizza into 1 piece, you do nothing because it already is 1 piece, so you “cut” 0 times. You cut 0 times when you divide by 1.
You already do nothing when you divide by 1, how do you do even less than that?
Thinking about slicing pizza is a useful analogy to understand division but it is also limited to positive integers. If you want to understand a little bit further what division means you have to think a little bit more.
In math, I can divide by any number that is not 0, which means that I can divide for example by 3.5.
What does that mean in real life to divide a pizza into 3.5 person ? Not much you could say. Actually, one way to look at it is that you could say 3.5 persons is actually three adults and one child that have to share the pizza, and that the child portion should be half the adult portion. That makes perfect sense. So when we want 1/3.5 of a pizza, what we want to get in our plate is the “adult portion” of a pizza divided into 3 adults and one child. Which will look like a little more than a quarter of a pizza.
Let’s go a little further, how should we interpret a pizza divided into 0.5 person ? Let’s take blindly the same analogy and see where it leads. It means that you want to share the pizza into a single child (who will get the entire pizza). Are we done ? Not at all ! If we really follow the same reasoning, 1/0.5 of a pizza represent the “adult portion” of a pizza divided into one children. So if I’m asking for 1/0.5 of a pizza, what I’m expecting in my plate (as an adult) is twice the child portion. And if the child is getting a full pizza, then it means that the adult portion will be TWO pizzas. Which means that dividing a pizza by 0.5 actually gives 2 pizzas !!!
Mathematically speaking, everything I said makes perfect sense. We indeed have 1 divided by 0.5 equals 2. But that’s where the analogy with pizzas break down. We can’t actually get more pizzas by slicing them, and we don’t magically get a bonus pizza if we give the first one to a child. So you need to understand that while the analogy is useful to understand division by integers, it cannot be used blindly.
When you start understanding this, you realize that when you divide (your pizza) by smaller and smaller numbers like 0.1 or 0.0001 , you will get something bigger and bigger ! Dividing a pizza by 0.001 means that you want the adult portion, knowing that a full pizza represent 0.001 = 1/1000 of a portion. So a pizza divided by 0.001 is 1000 pizzas.
And that should tell you that dividing a pizza by zero should not be one whole pizza. Intuitively, it should actually be infinitely many pizzas. But as we don’t like dealing with infinities, we prefer to let it undefined and avoid problems.
If you share a pizza with another person you have a half.
If you eat it alone you have one whole.
Before we share it between zero people let’s first think about what happens if we get closer to cutting it into zero pieces.
What would sharing it between 0.5 people or cutting it into 0.5 pieces mean? It logically follows that now there would be two wholes
The closer you get to dividing to zero the larger the result gets. 1 / 0.1 = 10, 1 / 0.01 = 100 etc
If you continue this logic it’s obvious that dividing anything by 0 is obviously infinite. So it’s undefined because infinity isn’t a real number but more like a concept. It would only be defined if you allow infinity to be used as a result.
But the main problem is that if you follow the same logic from the other direction. If you approach the solution from dividing by negative 1 first. 1 / -0.1 = -10, 1 / -0.01 = -100
So now dividing by 0 is obviously negative infinity. So it has two possible solutions that are equally valid, which means that the solution can’t be defined.
Dividing by 0 results in both positive and negative infinity at the same time, which is why it would cause the universe to collapse if we allowed people to divide by 0
By the way, division by zero isn’t undefined. It is infinity.
Think of division by 4. Each piece is of size 1/4. You have 4 pieces. Then think of division by 100. Each piece is 1/100. You have 100 pieces. Increase the number in a mental exercise. Division by infinity means each piece is 1/infinity. That is, cutting your pizza into slices that are each so thin that they have zero mass. How many slices will it take? Infinite. What is the size of each slice? Zero.
So 1/infinity = 0. Or 1/0 is infinity
Latest Answers