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
You can’t cut a pizza into ZERO pieces. If you don’t cut a pizza you have ONE piece.
Division by zero is undefined, because it leads to contradictions. You make 1/0 equal just about whatever you want and that makes it useless as a problem solving tool.
But it isn’t zero pieces, it’s 1 piece: the whole pizza.
There are many different ways of looking at what division is. One way is to look at it like repeated subtraction (in the same way multiplication is treated as repeated addition).
Let’s say we want to use the pizza to represent dividing 600 by 200. And let’s say, coincidentally, the pizza weighs 600 grams. So you subtract 200 grams but cutting off a 200 gram slice. That’s 1. There are 400 grams left. So you cut off another 200 gram slice. That’s 2. And now there are 200 grams left which you subtract for 3. 600 divided by 200 is 3.
Now let’s try that with 0. We want to divide 600 by 0. So we subtract 0 by cutting off 0 grams. There are 600 grams left. That’s 1. We subtract 0 from the remaining 600 grams leaving 600 grams behind. That’s 2. We subtract 0 from the remaining 600 grams leaving 600 grams behind. That’s 3. We subtract 0 from the remaining 600 grams leaving 600 grams behind. That’s 4. We subtract 0 from the remaining 600 grams leaving 600 grams behind. That’s 5.
I hope you can see where this is going.
From a more “pure” mathematical sense, when we say “A divided by B equals C” we are also, at the same time, saying that “B times C equals A.” So when B is 0, it messes up with that second part because anything times 0 is zero. Which either means nothing B could be would, when multiplied by 0, equal A (when A isn’t already 0), or *anything* B could be would, when multiplied by 9, equal A (when A is 0). Hence, *undefined.*
Division is multiplying by the inverse. i.e. If you say 6/3=2, that means 3*2=6. However, if you divide any number ny zero, you are saying there’s a number which multiplied by zero yields a number different from zero, which we know it’s impossible
There is no multiplicative inverse; you wind up with equations solved as 1=0 when you attempt to do define such.
If you didn’t cut it at all then it is in *one* piece, not zero pieces.
Try cutting a pizza into zero pieces and get back to us. That’s why it is undefined 🙂
Let’s try to calculate your example:
1) 1 divided by zero, how many times does zero go into 1? (no matter how many times you have nothing, will it never be equal to one)
2) Now after you have done the above, how much is left? (1 is left)
Repeat the above for all eternaty, and you’ll still have one left. 🙂
mathematically speaking
*anything* x 0 = 0
by reversing the multiplication into division (by dividing both sides by either 0 or *anything*) we can get
0 / *anything* = 0 and 0 / 0 = *anything*
(if you add so much nothing to nothing you still have nothing, if you try to divide nothing into pieces you still have nothing, if you try to measure how much nothing is in nothing you get a headache)
lets try a number divided by 0 with the assumption that a number divided by 0 does result in some number
*somethingA* / 0 = *somethingB*
if we reverse this division into multiplication (multiply both sides by 0) we get
*somethingA* = *somethingB* x 0
but we already know that any number multiplied by 0 becomes 0, so unless *somethingA* is 0 *somethingB* must somehow be something that does not give 0 when multiplied by 0, but there’s no number that can do that, hence undefined
Because that’s what mathematicians agree on. Math is just a set of rules that people agree on. Nothing stops you from defining your own set of rules where pizza/0 equals pizza. Mathematicians do that all the time (I mean, not divide pizza by 0, but create “new” sets of rules :)), and it is even sometimes useful!
If we agree to use this common set of rules to describe how many slices of pizza you get after cutting, we need to acknowledge that we won’t get an answer to the question “how many pizza slices we get if we divide it by 0”. It’s a shame, but on the other hand we can easily and reliably answer the question with any other number different than 0. And dividing pizza by 0 is like… Why would you ever need that information since it physically cannot be done anyway 🙂
> shouldnt it be still one whole pizza? Since I didn’t cut it so it’s still whole
That is actually division by 1.
[deleted]
Latest Answers