LOCK I DUN LIKE ZERO

[Dark]

What is 0/0? Well, let's take a gander at some other fractions.

 

1/1 = 1

2/2 = 1

3/3 = 1

4/4 = 1

5/5 = 1

 

...and it goes on and on, until it reaches ∞/∞.

 

But, let's look at some other fractions.

 

1/0 = UNDEFINED

2/0 = UNDEFINED

3/0 = UNDEFINED

4/0 = UNDEFINED

5/0 = UNDEFINED

 

...and it goes on and one, until it reaches ∞/0.

 

My question to the YCMers is, does 0/0 equal 1, or UNDEFINED?

[Akira]

How could that equal 1 >.>

 

Calculator says undefined.

[Kizzi]

lol DIVIDE BY ZERO *explosion*

[ragnarok1945]

technically it should be any number, real or imaginary

[Skuldur]

you can't divide by 0

[ragnarok1945]

yes you can, it'd just be undefined, although if the numerator is 0 as well it's different

[ragnarok1945]

yeah, from the calculator's answer. But if you think about it, any number multiplied by 0 is 0, so 0/0 should be any number you can think of (at least theoretically)

[LiAM]

you cant divide by nothing, try it with physical things like pie (hmm...)

 

i have 6 slices of pie, i divide them by 3 (3 ppl), 2 slices each ( 6/3=2)

 

 

i have 6 slices of pie, i divide them by 0 (0 ppl), 0 slices each ( 6/0=6) (6 left still)

[ragnarok1945]

actually it'd be infinite that way because there's 6 pieces of pie for 0 people, so each can have as many pieces of pie as he/she pleases.

[Catman25]

Yeah if you divide ANYTHING by 0, it doesn't work.

[problematica]

You can not divide a number by something that does not exist.

 

When you divide, you figure out how much of the numerator is in the denominator. If there is nothing in 0 that means that nothing can actually fit into that.

 

However, you can not define it as 0 because you can not put something into nothing so it does not actually not fit into it. Therefore, it is undefined.

[Jerry OldMaster]

Still I think it's silly. I can understand other fractions being undefined, but the 0/0 one..

Ah, now I see it.

The logical answer would be 1, like the OP showed. If we go into samples we pretty much get something like this: 0 cakes need to be divided by 0 people. Nobody gets anything, right? Ergo, 0.

So, we get two possibilities, so, we're stuck =D

 

Actually I'd prefer to leave this whole zero dividing thing as it is. It will merely cause problems if we try to prove something =P

[Guest]

Speaking as someone who has actually constructed rigorous proofs of everything from "0 * a = 0 for all a in Z" to the uniqueness of prime factorizations in Z, I can assure you that anyone with the slightest clue what they're talking about will respond "undefined".

[Dark]

I say the answer is one. You have 0 pieces of cake, and you have 0 people to give the cake to. Each person gets one piece of cake, since there are 0 of both factors. Same if it was one, there is one peice of cake and 1 person, each person gets one. But then there is the other side to it. You have 6 marbles, and 0 people to give them to. Each person can get as many marbles as he/she wants, but there are no people to give the marbles to, so each person gets ??? marbles. There is no number to define X/0, as long as X is not 0. But 0 divided by 0 has to be one, as it is a mathematical law that X/X equals one, regardless of 0 or not.

[Guest]

' pid='1440974' dateline='1228686590']

You have 0 pieces of cake' date=' and you have 0 people to give the cake to. Each person gets one piece of cake, since there are 0 of both factors.

[/quote']

 

Each person also gets 2 pieces of cake. While we're at it, each person gets negative twelve-and-a-half pieces of cake.

 

' pid='1440974' dateline='1228686590']

Same if it was one' date=' there is one peice of cake and 1 person, each person gets one.

[/quote']

 

Zero and one are fundamentally different. The former is an additive identity; the latter, multiplicative. They have different properties.

 

' pid='1440974' dateline='1228686590']

But then there is the other side to it. You have 6 marbles' date=' and 0 people to give them to. Each person can get as many marbles as he/she wants, but there are no people to give the marbles to, so each person gets ??? marbles. There is no number to define X/0, as long as X is not 0.

[/quote']

 

Through the use of limits, it is easy to see that, though X/0 for nonzero X has no defined value, its value is infinite in both the positive and negative directions. In other words, the limit of X/Y as Y approaches 0 where X =/= 0 is either positive or negative infinity. Infinity, remember, is not a value but a concept.

 

For this situation where X equals zero, however, it depends on the manner in which X and Y are being calculated, and in which they are approaching zero relative to one another. There is no way to go into more detail here without using calculus.

 

' pid='1440974' dateline='1228686590']

But 0 divided by 0 has to be one' date=' as it is a mathematical law that X/X equals one, regardless of 0 or not.

[/quote']

 

You are wrong. The mathematical law does not apply to zero.

 

Consider this: the definition of division states that A/B = C if and only if A = BC. This is not a property; it is a definition. Now, note that this means we are trying to find C such that 0C = 0. Any real number satisfies C; thus, no single C can be defined.

[Luna Lovegood]

If we consider Mathamatical law and apply it to 0, then we end up starting impossible stuff.

[ragnarok1945]

If we consider Mathamatical law and apply it to 0' date=' then we end up starting impossible stuff.

[/quote']

 

Why do you think imaginary and undefined numbers first began to arrive in the first place? We were applying much to 0

[Dark]

You have 0 pieces of cake' date=' and you have 0 people to give the cake to. Each person gets one piece of cake, since there are 0 of both factors.

[/quote']

 

Each person also gets 2 pieces of cake. While we're at it, each person gets negative twelve-and-a-half pieces of cake.

 

 

There are 0 people and 0 cakes. You cannot get 2 cakes, as there are only 0. Each person can get 1 peice of cake, since there are no people, and no cake to give. You cannot get a value of cake other than 1, because that value does not exsist.

 

Think of it this way, you have 3 cakes and 0 people. Each person, there aren't any, get's infinite peices of cake. Each cake is distributed to 0 people. But when it is 0 and 0, each person must get 1, as nothing else applies to it.

[ragnarok1945]

technically that's true, any number over the same = 1, but with 0 it's different.

 

You have 0 cakes, 0 people. Technically a person can take any number of cakes and the total amt will remain the same

[Valkyrie Lupia Blitzer]

You can't divide by zero.

 

Chuck Norris can.

 

Thus, 0/0 is undefined.

 

I want to change the topic, the question was already answered.

[Guest]

Look at it this way: the definition of division defines division as a binary function whose parameters are here called a and b. By the definition of division,

 

a/b = x <--> a = bx

 

And by a very basic theorem,

 

a = bx <--> a = b

 

Now, suppose b = 0. The equation "a = 0" is always true, regardless of x's value, if a = 0, and is always false, also regardless of x's value, if a =/= 0. Hence, division by zero always produces either no solution or infinite solutions. However, division is a binary function, and being a function it must always yield exactly one result, but when b = 0, the number of results is either zero or transfinite. Because of this, the cases where b = 0 are excluded from the domain of the function by definition.

 

This is why division by zero is always literally undefined: the cases where the divisor is zero are prohibited in the very definition of division, since the failure to make this prohibition causes division to cease to be a function.

 

If we consider Mathamatical law and apply it to 0' date=' then we end up starting impossible stuff.

[/quote']

 

I presume that you are referring to the logical fallacy of

 

If we consider Mathamatical law and apply it to 0' date=' then we end up starting impossible stuff.

[/quote']

 

Why do you think imaginary and undefined numbers first began to arrive in the first place? We were applying much to 0

 

Imaginary numbers came from the toolbox.

 

Up until a certain point in history, mathematics was used purely for its practical applications - calculating how to fling a stone so that it will hit a building, for example. However, a few centuries ago, mathematics exploded forward ahead of where it could actually be used, going in all sorts of seemingly useless directions. One of these was the set of imaginary numbers, heavily studied by Euler and Gauss, which were designed to account for the square roots of negative numbers. Later, when science expanded, scientists were able to look back through all the papers on formerly useless subjects, which gave them a "toolbox" to use on new fields of study; imaginary numbers, for example, are important in electricity and circuitry.

[Flinsbon]

OK, what about this one (more of a discussion).

___

V-1 is not a real number, but it must exist in the real world because it is one of the basic principals that transistors are created from. Without i, transistors do not work.

[Guest]

OK' date=' what about this one (more of a discussion).

___

V-1 is not a real number, but it must exist in the real world because it is one of the basic principals that transistors are created from. Without i, transistors do not work.

[/quote']

 

I assume that "V-1" is supposed to represent the square root of negative one? Use SQRT(-1) instead.

 

Anyhow, it is not an element of the set which has received the name "real numbers"; that does not mean that it lacks application to the real world.

[ragnarok1945]

You can't divide by zero.

 

Chuck Norris can.

 

Thus' date=' 0/0 is undefined.

 

I want to change the topic, the question was already answered.

[/quote']

 

Yes you can, the standard answer is undefined, but a theoretical answer is actually different (it's just that virtually no one sees such this answer)

[Flinsbon]

OK, since Crab Helmet answered my first one, here's another (similar to 0/0).

 

Any number^0 = 1

0^any positive number = 0

0^any negative number = let's not go there again.

 

Why is 0^0 undefined?