PID=0 = NOT C
Discuss.
So if I understand you correctly, you claim an alternate reality by simply making a set of numbers outside of the Real Numbers and then claiming that everything impossible with the Real Numbers exists there? I'm no math crack, so stop me if I'm wrong, but wasn't that known already? At least, I am pretty sure to have heard before that there is a realm outside of the Real Numbers (what you call NOT A) where dividing by zero, square roots of negatives etc. exist.
I'm not talking about real numbers v. unreal numbers. I considered that that was what I was talking about. I think we are looking at superpositional seperation.
Say one day you woke up and found that the number 1 was suddenly only related to 2 at superposition and had no other relationship to it. What would be the value of 1+1 if it didnt equal 2 except at Superposition?
As to creating new numbers - no. I think the numbers are already there - our own having limits that separate us from these 'other universe' numbers as it were.
Say one day you woke up and found that the number 1 was suddenly only related to 2 at superposition and had no other relationship to it. What would be the value of 1+1 if it didnt equal 2 except at Superposition?
Sorry, but I'm having trouble imagining that. After all, the value of two is arbitrary - it is defined by being 1+1. So two not being related to one is impossible, because that would rob two of its identity.
Perhaps it would help to spell out exactly what the question is, though. I assumed it was "Can we divide something by zero?", but that doesn't seem to be the case, so I'm having trouble as to where to start.
Assumedly the answer is there:
"Any value of A divided by zero equals NOT A (a number set unrelated to A except at superposition)"
But suddenly we are presented with the prospect of knowing what the value /A is equal to
because:
"PI (D=0)= NOT C (a circumference unrelated to circumference C except at superposition)"
Suddenly the Pi of an object with zero diameter has a value indicating a solution to A divided by Zero.
What object has a diameter of zero and a PI value equal to its alternate reality circumference? A singularity?
If the big bang theory applies here: then I, in interacting with Pi at D=0, am interacting with exotic possibility from my own universe. Does the Universe go boom just for doing maths?
Hmm... I see. If I understand correctly, Math is hard.
sorry but first, since english is not my mayn lenguage, could you please define "superposition" more clearly, beside all the rest that is notclear at all.
then I kind of understand how an undefined limit can give as a result a set of numbers, the function diverges to a given set of numbers, for example, n belongs to positive natural numbers N:{1,2,3,4,5...}, with n<10 , n->10, the function (-1)^n does not converge and gives aset of results of 1 and -1.
the problem is, first for a function to have a soltion, the function MUST converge, so the only set of solutions a convergent function can have is a set of a single element (a group with a single element).
second, there is a misconception with the function used, yes, Pi=P/r (where P is the perimeter of a circunference or radius r), but that function is definde for {r E R/ r>0} (r belongs to real numbers, with r strictly bigger than zero), sowhen you do Pi=P/r with r=0 you are using a undefined function, to say divided by zero is defined.
second, there is a misconception with the function used, yes, Pi=P/r (where P is the perimeter of a circunference or radius r), but that function is definde for {r E R/ r>0} (r belongs to real numbers, with r strictly bigger than zero), sowhen you do Pi=P/r with r=0 you are using a undefined function, to say divided by zero is defined.
QFT.
What it seems to me is being done here is something like the following: dividing by zero is forbidden in normal mathematics. But you know what, let's create a realm where it works anyway (which, in math, is legitimate), and where x/0 is defined for a number of that realm. And then, you suddenly use this very premise this new realm is based upon to "prove" dividing by zero works in your new system - though that is what said system is based on to begin with.
As to the real vs. unreal matter: to me, this seems very much what this is about. Correct me where I'm going astray here, but look at what you do: you divide A/0. This function is defined for , but a real number may not be divided by zero, so you (or whoever wrote this) makes up a new system for which this function is defined, then does the math, and then realizes that the result is, indeed, part of his new system - which, put plainly instead of in geeksp33k, was pretty obvious to begin with.
I spotted a divide by zero fallacy!
f(D) = C/D
f(D) = Pi, where D is different from 0
however, what you're trying to do is calculate 0/0 forgetting that there was in fact a relation between C and D. however, there WAS a relation, hence your conclusion is incorrect
I'll use an other example: 2 is the ratio of a number N and its double D
2 = D / N
Following your train of thoughts you conclude that 2 is not a number but a collection of numbers
In Real math, we divide by zero like this:
limD->0 C/D = Pi
limx->0 0/x = not defined
and BTW: NOT A (if A as a member of R, the collection of real numbers) is defined as this:
NOT A = R union { positive infinity, negative infinity } if A is not zero, and
NOT 0 = {"not defined"} (any number is possible at the same time)
mispost, see two posts later.
nevermind my post got eaten
Okay, I'm in Algebra II. I'm trying to wrap my head around this. Or is this more of a physics/algebra question? Bah I'll shut up since it's 0750. BUT! 1+1=3. Simple as that. ;) And since I brought up physics (I'm trying to get my brain crankin')..
It is said that there are two absolutes in the universe: space and time. Anyone who knows the definition of each can't explain it, and anyone who can explain the definition doesn't know it. This is probably because you cannot refer to one without referring to the other (in essence, space is part of Time's definition and time is part of Space's definition). Time to get off definitions now. If there are two absolutes, why does it seem like there is a third? Binary has choices that are definitive, the answer is either yes or no, the object either is or isn't. This is represented via the 1s and 0s used in binary.
Have I confused you yet? Because I just confused myself.
Actually i reached a conclusion regarding space and time in 2004.
- The Universe is debris of change in possibility.
- Time is continuous change in possibility.
- Singularity is moment of change in possibility.
Basically it invalidates Religion and Evolution - what else were we going to expect?
So I am looking for mathematical solutions.
Actually i reached a conclusion regarding space and time in 2004.
- The Universe is debris of change in possibility.
- Time is continuous change in possibility.
- Singularity is moment of change in possibility.
Basically it invalidates Religion and Evolution - what else were we going to expect?
So I am looking for mathematical solutions.
Whoa whoa whoa, easy there. Don't you think that's a bit lazy, throwing around a few magniloquent words describing completely trivial facts, and then claiming to have disproven Religion and Evolution?
The proof is erroneous. a circle is defined as a two dimensional shape. as d -> 0 the circle -> a point (0 dimensional construct). As it is no longer a circle Pi = C/D is no longer applicable. QED
edited: missed the similar below - my apologies. and for the poster a couple back - and once upon a time germs didn't exist, all because we didn't have the technology/understanding to observe them. Moreover, if you've never seen a microbe, why are you so sure they exist? Oh, that's right because someone told it to someone, and the proof was sufficient for belief. Or, of course, you can take the scientific approach, and see what is really out there - some places to start, if you're a serious student: anthropology, archaeology, astronomy, of course, that assumes you are at least familiar with the 7 liberal arts and sciences. In fact, I find it fascinating that as we increase our level of understanding, more of the old stories make sense. There was an excellent show on the human family tree the other day - interesting, but I believe off with some of the assumptions they espoused as far as genetic changes happening at set intervals, as it totally discounted the notion of punctuated equilibrium.
OK, time for some answers.
Division by zero
First, there are (I believe) eight qualities that define something as being an "algebra". I will do my best to recite them from memory.
A set A is an algebraic set if it has the following qualities:
1. There exists an operation "+" (which can be referred to as addition or whatever you wish...) such that for every a and b that are elements of A, a+b is also an element of A.
2. There exists an operation "*" (which can be referred to as multiplication or whatever you wish...) such that for every a and b that are elements of A, a*b is also an element of A. (Note: maybe multiplication is not included...)
3. There exists an element of A referred to as "zero" or "0" such that a+0=a for every a that is an element of A.
4. There exists an element of A referred to as "Identity" or "1" such that a*1=a for every a that is an element of A.
I believe the other 4 properties have to do with reflexiveness (a=a), symmetry (a+b=b+a), being associative ( (a+(b+c))=((a+b)+c) ), and distribution ( a*(b+c)=a*b+a*c ) but I am not sure. Also note that in this definition a*b is not required to be the same as b*a. An example of this can be seen in vector algebra where A*B= -B*B. I may have missed something but I think that is it. Now, if one chooses to be very creative in one's definitions one can prove that silly sets can be made into algebras but that is mathematics for ya. 
The important point to note that addition and multiplication are defined but subtractiuon and division are not defined. In the sets of numbers that we normally use subtraction is a shortcut method for adding the negative of a number and division is a shortcut method for multipying by the reciprocal of a number.
When working with ordinary numbers one cannot "divide" by (multiply by the inverse of) zero because the inverse of zero is not an element of the set of numbers being used. Can one define such a number to create a new set? Sure, but unless one can find a need to it is a wasted effort. The reason proofs are made to determine whether or not something can be defined as an algebra is so that one can use the rules of algebra to determine things using matemeatics. If one has nothing to determine then there is no use to do it.
About imaginary numbers
It should be noted that "imaginary" numbers are not really imaginary and thus creating a number to be the answer to what one gets when dividing by zero would not be using an imaginary number.
They ("imaginary" numbers) developed because when studying various real processes it was determined that relations existed between them and that by applying certain definitions the relations could be made into an algebra and thus useful things could be determined using the rules of algebra. (Ugly sounding sentence. Uggh!)
Take electromagnetic theory as an example.
There are electric fields and there are magnetic fields. If you add two electric fields together you still get another electric field. If one multiplies them together using the cross product one will get the zero term...The magnitude of the energy contained is related to the magnitude of the field. The same is true for magnetic fields. Also, electric fields do not add together with magnetic fields. Their components remain distinct. However, the energy contained in a field that has both will be related to the square root of the sum of the squares of the two fields. It is like the hypotenuse of a triangle in that regard. It will be the square root of a2+b2 where a and b are the magnitudes of the electric and magnetic fields.
Further, if you have a field that contains both electric and magnetic fields and add it to another field that contains both electric and magnetic fields the sum of the fields can be found by adding the components. The new electric field component of the combined field will be the sum of the two electric fields. The new magnetic field component of the combined field will be the sum of the two electric fields.
When examining the mathematics involved some things were determined. First if you seperated the magnetic and electric fields with a "J" in front of the magnetic field to keep its terms separate the field could be expressed as follows: a+Jb. Then adding two fields would be (a1+Jb1)+(a2+Jb2)=(a1+a2)+J(b1+b2) to represent keeping the fields separate. (But wait, that looks like the addition of complex numbers!) Now, how can we find a formula that will give the magnitude for a combined field listed above? Use the following to make the middle terms disappear: (a+Jb)*(a-Jb). Using algebra, the result is a2 _J2b2. But, the answer we are looking for is a2+b2. So, defining J, the term which was introduced merely to keep the two terms separate, as being a number which when squared gives -1 will give a2+b2. An algebra that lets one describe how electric and magnetic fields interact has now been created and with it "i".
It is no different than how we came up with the numbers 1 and zero and al the otrher numbers we use. It filled a need and so we deifined it. Once there was a need to define "J" (more commonly referred to as "i") as a number that when squared would equal -1, an algebra was created and by determining the ins and outs of this new algebra the characteristics of the fields could be predicted and determined. Also, there have also been found many more things that meet the requirements to be complex numbers and thus the uses extend beyond electromagnetic theory.
The Circle with a radius of zero
A circle is defined as the locus of all points within a plane which are all the same given distance (the radius) from a given point (the origin).
So, if the distance, or radius, is zero then the locus of all points in that plane whose distance from the given point (the origin) is zer would be the origin itself. So, technically a point can be considered a circle all by itself but we don't bother with what can be determined from that definition because it has no use to us.
It may be appropriate to say that the circumference of this point is "zero" but then pi=C/2r. r is undefined and thus you cannot determine pi from this because division by zero is undefined because the reciprocle of zero is undefined. In actuality, pi is determined as a limit. The value of the circumference is calculated with approximations determined by placing polygons within (or without) the circle (I think the proper terms are inscribing and circumscribing, no crude comments related to word similarity please) and calculatng their perimeter. Then as one finds the limit of the value as the number of sides approaches infinity one can find pi.
edit note: what I was referring to as an "algebra" is the definitionof a vector space. My apologies on that.
We define a set V to be a vector space if
- x+y=y+x for each x and y in V
- x+(y+z)
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=(x+y)
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+z for each x, y, and z in V- There is a unique "zero vector" such that x+0=x for each x in V
- For each x in V there is a unique vector -x such that x+(-x)
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=0.- 1x=x
- (c1c2)
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x=c1(c2x)
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for each x in V and c1 and c2 in ℂ.- c(x+y)
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=cx+cy for each x and y in V and c in ℂ.- (c1+c2)
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x=c1x+c2x for each x in V and c1 and c2 in ℂ.
note: I believe the "c" refers to the set of complete numbers or perhaps complex numbers, but I think complex would be reresented by Z.
Basically, the algebra of numbers meets the definitions of a vector space. The important point being that addition and multiplicaton are defined but not subtraction and division. Thus there is no definition for division by zero as the reciprocle of zero is not defined so that a number can be multiplied by it.
OK, a mathematical sollution? the answer is 0/0 (since C=0 and D=0 that's what you're doing) is any and all numbers at the same time.
Sounds complex? well it actually isn't: Dividing is defined as the inverse of multiplication. 6/2 =3 only because 3*2 = 6. THIS IS VERY IMPORTANT TO REMEMBER
6/2 exists and we call it 3, because 3 * 2 is 6
However, There is no real number that we can multiply by 0 to get 6. "x*0=6" doesn't have a real sollution. But if 6/0 would exist, then 6/0 would be a number infinitely large (positive or negative). We can see this because of interpolation (6/1 = 6; 6/0.1 = 60; 6/0.001 = 6000 etc, while 6/-1 = -6; 6/-0.1 = -60; 6/-0.001 = -6000). The closer we come to 0 the extremer the result becomes.
Conculsion: the size of NOT 6 would be exaclty 2: mathematicians call those numbers positive and negative infinity
However, if we look at 0/0 instead of 6/0, we get a special case: it doesn't do the same as 6 or any other number: multiclication of any number with zero gives the same result: zero. unlike "x*0=6" (where x can't be a real number), we have the equation "x*0=0", a.k.a. x could be any number (2*0=0; 3*0=0; ...), hence 0/0 can be any number.
Conclusion: the size of NOT 0 would be exaclty the same size as the collection of real numbers
Savy?
So:
D=x, C=y, C/D=z only because z*D=C (it's how 'divide' is defined)
D=1, C=3.14..., C/D = 3.14... only becasue 3.14... *1 = 3.14...
D=0.5, C=1.57..., C/D = 1.57... only becasue 1.57... *1 = 1.57...
now for the zero case
D=0, C=0, C/D is a number for which the following applies: 0* C/D = 0.
So if we make a graph of C/D, we will see the a line where Y is 3.14 (for, lets say D=3, then the fuction's answer is 3.14), and the entire Y axis (where X is zero) will also be collored by the graph. (when the radius is 0, the C is in fact not only PI times the radius, but also 4 times, 6 times and even 2000 times)
- I tried to be as clear as possible. if there aren't things you don't understand about my explenation, feel free to ask
"x*6=0" doesn't have a real sollution.
You mean "x*0=6", I assume? Other than that, kudos to you and Rumplestix for actually putting work into a mathematical proof, but I honestly think this is unnecessary - yellowdingo's argument, assuming he isn't just being facetious, is fallacious by flaw of logic (premise proving premise) rather than by mathematical mistake.
"x*6=0" doesn't have a real sollution.
You mean "x*0=6", I assume? Other than that, kudos to you and Rumplestix for actually putting work into a mathematical proof, but I honestly think this is unnecessary - yellowdingo's argument, assuming he isn't just being facetious, is fallacious by flaw of logic (premise proving premise) rather than by mathematical mistake.
I did notice that and ignored it.
I just couldn't pass up on the chance to mention vector spaces and explain why imaginary numbers aren't imaginary.
Generally when x/x happens in fraction, you reduce the fraction instead of leaving it in to try to force a conclusion that wouldn't otherwise be reached. In this case, you lose the 0/0 and move on.
Generally when x/x happens in fraction, you reduce the fraction instead of leaving it in to try to force a conclusion that wouldn't otherwise be reached. In this case, you lose the 0/0 and move on.
Not true. There is no forcing going on. That is what is referred to as a removable discontinuity. It can be factored out but it is still a discontinuity and cannot be ignored. It must be included when determing the domains of functions. the function X2/x is equivalent to the function f(x)=x for all points not equal to 0. For zero it is undefined. In every math class I have eveer taken, an answer that did not exclude 0 from the domain would be considered wrong because it is wrong.
Not true. There is no forcing going on. That is what is referred to as a removable discontinuity. It can be factored out but it is still a discontinuity and cannot be ignored. It must be included when determing the domains of functions. the function X2/x is equivalent to the function f(x)=x for all points not equal to 0. For zero it is undefined. In every math class I have eveer taken, an answer that did not exclude 0 from the domain would be considered wrong because it is wrong.
Right, and nothing meaningful can be dreived from OP's calculations. π is a ratio and a constant and in OP's case it's being multiplied by 0 and divided by 0 (the circle's circumference and diameter, respectively). From this OP draws a totally lolmaths conclusion. Am I the only one who doesn't think this is cute?
Actually i reached a conclusion regarding space and time in 2004.
- The Universe is debris of change in possibility.
- Time is continuous change in possibility.
- Singularity is moment of change in possibility.
Basically it invalidates Religion and Evolution - what else were we going to expect?
If this is true, I assume you've published a peer-reviewed essay on the subject. Why hasn't the scientific community adopted your revolutionary theories on evolution that disproves a phenomenon that has on numerous occasions been observed?
I did indeed mean "x*0=6". I'll edit it
Generally when x/x happens in fraction, you reduce the fraction instead of leaving it in to try to force a conclusion that wouldn't otherwise be reached. In this case, you lose the 0/0 and move on.
I have thought of that, but here this is not the case: the OP wants to map f(x) = (π*x)/x, not f(x) = pi. And one can't simply f(x) = (π*x)/x, since x can be zero (you can't remove the x/x part if x can be zero)
and as explained: when one maps f(x) = (π*x)/x, at x=0 you will have a vertical line, as for any real number y applies "y*0=0"
Generally when x/x happens in fraction, you reduce the fraction instead of leaving it in to try to force a conclusion that wouldn't otherwise be reached. In this case, you lose the 0/0 and move on.
Not true. There is no forcing going on. That is what is referred to as a removable discontinuity. It can be factored out but it is still a discontinuity and cannot be ignored. It must be included when determing the domains of functions. the function X2/x is equivalent to the function f(x)=x for all points not equal to 0. For zero it is undefined. In every math class I have eveer taken, an answer that did not exclude 0 from the domain would be considered wrong because it is wrong.
Well since string theory proves there are more than 10 dimensions why couldn't there be more dimensions than 2 to numbers. We have negative numbers and postive numbers, why not have a dimension of numbers called the zero dimension of numbers? Just as a negative times a positive is equal to a negative, and a negative times a negative is equal to a positive, and a positive times a postitive is equal to a postive. Why can't a zero axis number times a positive number be a zero axis number (appearing to be just plain zero where all three axis's meet). So then you get anything times a zero axis number is equal to a zero axis number. Because we haven't defined these numbers they will always appear to be zero. So lets say our zero axis is called Z. So we have 5Z * 2 = 10Z, or 10 on the zero axis. Then when we go to divide by zero we can get a 'not A' number. So say we have 10/0 = 0Z/10 * 10/0 = 10Z/0 since zero lies on the zero axis we get 10Z or ten along the zero axis. Now as we now if this were part of a bigger equations say 10 * (10/0) then anything multiplied by a Z is equal to Z so we would get 100Z or 100 along the Z axis.
Though as it has been pointed out I'm not entirely sure where this would be useful. I'm really not sure if I did that right. Hmm, maybe we can use this to figure out that prime problem.
I just couldn't pass up on the chance to mention vector spaces and explain why imaginary numbers aren't imaginary.
Now that is a sentiment I can accept :D.