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
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.
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