conway

Still treating people with passive aggressive superiority I see. I suppose you think "facts" are unchangeable? Case in point....Greek ellipses...case in point flat earth.....facts can be challenged....OldchemE has the right to do so. Sure if he hadn't have argued with you after your first reply things would have been great huh Strange? That said .999...is = 1.....in my opinion. But I appreciate and will continue to listen to the op and his/her ideas with out being a jerk.

Amplitude Fore Warning This idea is not new to this or other forums. No one here agrees. Most consider me a crank. There has been several positive reviews. I am willing to talk in length if you wish "only on topic"....but the "lurkers" here will soon bite with seething comments about me. Relative Mathematics It is the inherent nature of all things that they are a compilation of two different and distinct things. It is axiomatic that these two things are space and value. The value of any given thing being what it is, while the space is what it occupies. It is true that, abstract or otherwise numbers are a thing, therefore they must also contain a compilation of space and value. It is an axiomatic truth that space is the labeling of quantities of dimensions. It is an axiomatic truth that value is the labeling of quantities of existence, other than dimensions. It is an axiomatic truth that space and value exist in one of two forms. So that any given quantity of space or value is first labeled as defined or undefined. It is reasonable to say that any given number, that has had both its quantities of space and value labeled as undefined, requires no further question as to its nature. If however a given number, has had both its quantities of space and value labeled as defined, it is then necessary to further define the given quantities. That is to say what is the nature of the space and value's that are defined. There are four axiomatic steps in the further defining of a defined quantity of space and value. First it is that, after a given quantity of space and value is labeled as defined, a symbol is given to identify the amount of quantities given. Second it is that the given amounts of defined space and value are labeled as finite or infinite. Third it is that the given amounts of defined space and value, that are finite or infinite, are labeled as fractional or whole. Fourth it is that the given amounts of defined space and value, that are finite or infinite, fractional or whole, are labeled as positive or negative. It is the case that all forms of the defining of quantities of space and value, are from the perspective of our humanity. This then shows that there is a collection of only four kinds of numbers. That is there are numbers that possess an undefined space and an undefined value. Otherwise represented as a ( Uv + Us ). Such a number not requiring further defining. There are numbers that possess a defined value and a defined space. Otherwise represented as a ( Dv + Ds ). Such a number requiring further defining. There are numbers that possess a defined value and an undefined space. Otherwise represented as a ( Dv + Us ). There are numbers that possess an undefined value and a defined space. Otherwise represented as a ( Uv + Ds ). It is reasonable to say that natural numbers have both their quantities of space and value labeled as defined. That is that a natural number is a ( Dv + Ds ). It is then through the process of further defining, that a natural number such as 2 is labeled as having ( 2Dv + 2Ds ). The symbol 2 then is the symbol identifying the amounts of quantities contained. It is then that the given quantities are labeled as finite. Otherwise represented as a ( 2DvF + 2DsF ). It is then that the given quantities are labeled as whole. Otherwise represented as a ( 2DvFW + 2DsFW ). It is then that a positive is assigned to the compilation of space and value, and it is so on for any natural number. It is also the case that fractions are labeled as a ( Dv + Ds ). That is any given fraction has both its quantities of space and value labeled as defined. So that such a number as .2 is labeled as ( 2DvFF + 2DsFF ). Then a positive is assigned to the compilation of space and value. Additionally, a fractional symbol may replace the decimal symbol. It is also the case that infinite numbers are labeled as a ( Dv + Ds ). So that such a number as 2infinite is defined as a ( 2DvIW + 2DsIW ). As well as fractional infinites, such as .2infinite. Which is labeled as ( 2DvIF + 2DsIF ). Then a positive is assigned to both compilations of space and value, and it is so on for any infinite or fractionally infinite number. Remaining are numbers that are a ( Uv + Ds ) and numbers that are a ( Dv + Us ). Such numbers do not necessarily require further defining. As an undefined quantity of space or value composites the given number. So then such numbers can only be limitedly defined relative to the given defined quantity. If then a number possess a defined value and an undefined space, the sum is then relative to the defined value. So that such a number as ( Dv + Us ) is then a 1 relative. Otherwise represented as a 1r. If then a number possess an undefined value and a defined space, the sum is then relative to the defined space. So that such a number as a ( Uv + Ds ) is then a zero. As no quantity of value is defined, and as one quantity of space is defined. The space of zero is clearly defined on any number line. The equation ( 1 + (-1) = 0 ) proves this in that, if zero did not occupy a defined space on the number line, then the equation would equal ( -1 ), and not zero. It is the case in multiplication and division, that neither number given is an actual number. Not in the fashion that each symbol contains both space and value. It is that one symbol is representing a value, and that one symbol is representing a space. It is the case that in multiplication the labeling of the given symbols as space or value in a specific order is not necessary. The sum yielded is always the same. It is the case that in division the labeling of the given symbols as space or value in a specific order changes the sum that is yielded. So that as an axiom the first given symbol is labeled as value, while the second given symbol is labeled as space. It is then that in multiplication the given value is placed additionally into the given spaces. Then all values are added in all spaces. It is then that in division the given value is placed divisionally into all given spaces. Then all values are subtracted except one. So that in the equation ( 2 x 0 = X ), there is a given defined value of ( 2DvFW ), that is placed additionally into the given defined space of ( Ds ). Then all values are added in all spaces. This process then yields the number 2. Whereas the equation ( 0 x 2 = X ), there is a given undefined value of ( Uv ), that is placed additionally into the defined space of ( 2DsFW ). Then all values are added in all spaces. This process then yields the number zero. So then in the equation ( 2 / 0 = X ), there is a defined value of ( 2DvFW ), that is placed divisionally into the defined space of ( Ds ). Then all values are subtracted except one. This process then yields the number 2. Whereas the equation ( 0 / 2 = X ), there is an undefined value of ( Uv ), that is placed divisionally into the defined space of ( 2DsFW ). Then all values are subtracted except one. This process then yields the number zero. As an addition to all current field axioms these ideas are expressed as stated. " For every A in S there exists a Z1 and Z2, constituting A, such that any A in operation of multiplication or division is only representing Z1 or Z2 in any given equation. Such that Z1 for all A's other than zero equal A. Such that Z2 for all A's other than zero equal A. Such that Z1 for zero equals zero. Such that Z2 for zero equals 1. " It is possible that further defining of the given defined value of a relative number, and the given defined space of a zero, is applicable and necessary. It is possible to either leave the same, or adapt exponents and logarithms. Naturally further axioms will be needed for adaption. Such as exponents of zero existing as a space representation of zero (z2). Logarithms of zero existing as a value representation of zero (z1). It is possible to here-in re-address the idea of the continuum theory. If the definitions for numbers and their groups, are adapted as stated, and with further exploration into the defining of ( Dv + Us ) relative numbers, ( Uv + Ds ) zero numbers, ( Uv + Us ) undefined numbers, and their placement onto the number line. The idea here being to show all numbers originating from and returning to ( Uv + Us ) on any given number line.

Amplitude Thanks for your interest. I've been taking a brake from the forum's. They can be quite stressfull...and people can be very rude. Are you seriously interested then?

Axiom Let every number be arbitrarily composed of two numbers. Let the number table exist as such… 0=(0,1) 1=(1,1) 2=(2,2) 3=(3,3) 4=(4,4)…and so on Let no "ordered pair" be represented by another "further" ordered pair. Let the first number of the number chosen be labeled as z1 Let the second number of the number chosen be labeled as z2 Let multiplication exist as follows… (A x B) = ( z1forA x z2forB ) = ( z2forA x z1forB ) = ( z1forB x z2forA ) = ( z2forB x z1forA ) Let division exist as follows… (A/B) = ( z1forA/z2forB ) (B/A) = ( z1forB/z2forA )

Postulates 3 = ( ( 1,1,1) “placed into” (_,_,_) )= (1,1,1) 2 = ( (1,1) ) “placed into” (_,_) )= (1,1) 1 = ( (1) ) “placed into” (_) ) = (1) 0 = ( (0) “placed into” (_) ) = (0) So that ( 3 x 2 ) is… Either (1,1,1) or (_,_,_) for 3 And Either (1,1) or (_,_) for 2 (but NOT both for each, and only the opposite of each, in any binary expression) Then…. (1,1,1) placed into (_,_) then added Or (1,1) placed into (_,_,_) then added So that in binary operation by 0 ( 2 x 0 )…is (1,1) placed into (_) then added Or (0) Placed into (_,_) then added

uncool There is a z1 and a z2 in 1 = 0. If I define it as so. Yes to be specific I must say 1 (as z1) = 0 (as z2) 1 (as z2) (not=) 0 (as z1) I agree I am not using "usual" assumptions of logic......perhaps this is my greatest issue. I however see no issues with the following statement being logical..... 1 (is and is not) equal to 0. In the same way that a particle can be in a state of superposition.

Bignose I hope you understand that I do understand what it is you are trying to tell me. You insist.... "It is imperative that I show a way to label a specific "thing" as z1 or z2". I do not feel this way. I think that it is inherent. It does not need to be shown. And I agree you have given an example that shows how it leads to "wrong" answers. I also showed you examples how it can lead to the "correct" answers. GRANTED only because " I " chose z1 and z2 accordingly........... I have found that 99 percent of the time I disagree with someone it is because of a lack of understanding on my part. I am sure this is the case here. But until I can see your perspective as valid ( as yet I can not) there remains no reason to continue on this line of debate. Much thanks for your consideration! Uncool I can not assign meaning to something for you. Either you find something meaningful or you do not. I can talk semantics...."apples" and so on....but I'd rather not. I HAVE concluded that 1 = 0. Only as if zero is used as z2. If zero is used as z1 it is NOT equal. This in and of its self should show you the "usefulness". Again if you do not agree...I can not change that. Perhaps I can change my perspective on the matter...that I can do....perhaps you can offer me reasons why ( 1 = 0 and 1 ( not =) 0 ) can not BOTH be true.......as I am stating.

Bignose I placed the words ball and velocity next to each other in order to suggest that it does not matter which is labled which. Perhaps not the most efficient means of communicate as it has lead to misunderstadings here. I do not understand where you think I have implied an object moves or does not move over zero time. I have never labeled time as zero. Is there some reason why you feel that human consciousness can not chose which to label z1 and z2. Is there some rule stating human consciousness is NOT a factor in mathematics. It certainty appears so to me. Again there is no need to argue over which is z1 or which is z2......either labeling is correct....we chose relative to our needs. In any case I will consider what you have suggested to me and contain to ponder.... thank you for your time uncool ok.......rewrite the axiom to be a "secondary" form of multiplication, in addition to the original. I see that this changes nothing. As to it's usefulness.....and examples as to it.........that should be obvious. The equations already posted up to this point show how to satisfy the axiom. If I tangibly held apples in my hand and multiplied them by zero I still hold apples in my hand, and so on.....

I agree its provable from the field axioms that 0 times anything is 0. I suggest that the opposite is also true....with the given "proposed" axiom. So then both statements are true in any given field. Is there anything proving or suggesting that BOTH statements can NOT be true. (obviously not at the same time)

wtf I agree 0 times anything is 0. I also showed that eqution as exisiting as true. I am also suggesting that 0 times anyting is anyting.

Bignose I gratefully appreciate your reply and time. It is possible to not consider space or value at all. I have only done so in hopes that it may help me communicate with Wtf. It is possible to always and only say z1 and z2. Perhaps as you point out it is best to continue to do so. If not I will always refer back to post #12 for the defentions for space and value. That has not changed from other uses of them by me. It is my opnion that z1 and z2 is inherent in the eqution. For example.... If neither z1(velocity/ball) or z2(velocity/ball) equal zero, than it does not matter which is z1 or z2 the sum is always the same. If either z1(velocity/ball) or z2(velocity/ball) equal zero, it then is inherent in the equation. If I have 1 ball traveling a velocity of 0. Then inherently the ball is the z1, the velocity is z2 1(z1) x 0(z2) = 1 (ball) If I have 0 ball traveling a velocity of 1, Then inherently the ball is z1, velocity is z2. 0(z1) x 1(z2) = 0 (ball) "If I have" is the semantical argument dictating "value, z1" or "space, z2". If again as I agree we should stay away from semantics then z1 is and z2 are simply chosen based upon the needs of the mathematician. All four equations are true, relative to what is defined z1 or z2, at the will of the observer. A x 0 = A ​0 x A = A A x 0 = 0 ​0 x A = 0

Studiot I would like to repeat back to you what it is I "think" you are trying to tell me, in order I hope to better communicate with you. You are saying that all current field axioms can be shown to exists with "non numberic values". That is (A,B,C), and or (squiggly lines, and triangles). If this is so then my reply is as follows. The proposed field axioms states that z1 and z2 for A's or "any non numberic value", OTHER THAN zero, equal A or (squiggly line, and triangle). So I can not show any operations differently than how they already exist, unless you distinguish a given A or (squiggly line, and triangle) as zero. If then you do the proposed field axiom becomes relevant and I can show you an operation containing an A, or (squiggly line, and triangle.) wtf So then regarding zero and 1. z2 for 1 = 1 z2 for 0 = 1 z1 for 1 = 1 z1 for 0 = 0 So then philosophically or semantically I am saying The space of zero and 1 are equivalent The value of zero and 1 are not equivalent Depending on whether zero is used as value, or as space, in any binary expression, determines the sum of the expression. Or 0(z1) x 1(z2) = 0 1(z2) x 0(z1) = 0 1(z1) x 0(z2) = 1 0(z2) x 1(z1) = 1 A(z1) x 0(z2) = A 0(z2) x A(z1) = A

wtf We then apply to actual binary expressions. We should start with non zeros. If then the expression is ( 2 x 3 ) We declare "according to the proposed axiom" that neither symbol given is a number....rather that one symbol is z1 and one symbol is z2 As the commutative property exists, it does not matter which is labeled which. So then...... ( 2(is actually z1) x 3(is actually z2) ) where z1 for 2 is 2, z2 for 3 is 3.....we then return to an expression of 2 x 3 so again regarding non zero's this seems pointless....albeit functional........ I will hold here before addressing 1 and zero......to ensure we still remain on the same page.... It may be helpful to consider z1 and z2 by there philosophical names as opposed to there mathematical z1 = abstract value without space z2 = abstract space without value space = a labeled quantity of dimension value = a labeled quantity of existence other than a dimension. where as when a value(z1) is "placed" into a space(z2) a "NUMBER" is generated. again in addition and subtraction z1 and z2 are NOT separated.

wtf Excellent response! Thank you! z1 and z2 are NOT elements in a field. It is that they are elements of an element in a field. So then if 1 is an element in a field, then 1 is composed of the two elements z1 and z2. So then if A is an element in a field, then A is composed of the two elements z1 and z2. In all cases of A (not being zero) then z1 and z2 are both A. It is the case in addition and subtraction that the elements of an element are both inherent in the number, and are NOT separated. That is to say addition and subtraction stay the same. It is only in a binary expression of multiplication and division, that z1 and z2 of an element are separated. I hope this is clearer. I can continue to discuss the multiplication and division of z1 and z2 supposing I have clarified these earlier topics...... Thanks

wtf I feel that Studiot and myself merely had a slight misunderstanding. Thank you for the support. I would also point out that the proposed axiom has no relevance to addition or subtraction. Were the examples I gave you sufficient? I can try to be more specific. Do you have any more curiosity in this regard? If not I understand and thank you for your time. studiot If I may say again. z1 and z2 for any "non numeric element" is the element itself. That is to say z1 for A is A z2 for A is A so then if no zero is defined..... there is no relevance to the given proposed axiom. I can not use the field as you gave it to either prove or disprove this proposed axiom. I hope I am not still misunderstanding you. I can show how it still works...but this then is a pointless exercise, as I am sure you can see......it only becomes relevant regarding zero.

studiot I apologize. If then the four elements given by you are A,B,C,D........and if then you chose to not define any element as a zero, then the answer to your question is.... There is no new affects by this axiom... Are you suggesting that I must adapt it? The axiom is specially designed for the use of zero in binary expressions of multiplication and division. If then the variables in an equation or expression are not zero... no adaption is possible...or necessary. I hope you will continue to help me....at least for a while. The axiom only yields new results regarding binary expressions of zero. It does so... in such a way as to leave all other expressions and equations the same. I hope I have done a better job of understanding and answering your question. I appreciate your time and patience studiot.

wtf a rational example .5 contains (.5 z1, and .5 z2 ) a real example 2 contains (2 z1, and 2 z2) a integer example -1 contains (-1 z1, and -1 z2 ) studiot If the "non numeric elements" are not zero... no new affects occurs. If the non numeric elements are zero, then the multiplication of reals by zero become relative to which non numeric element is z1 and which is z2 in the given binary expression. For example A = any numeric element other than zero 0(z1) x A(z2) = 0 0(z2) x A(z1) = A

As an addition to all current field axioms. "For every A in S there exists a z1 and a z2 constituting A. Such that any A in operation of a binary expression of mulitpilcation or divison is only representing z1 or z2. Such that z1 and z2 for all A's other than zero equal A. Such that z1 for zero equals zero. Such that z2 for zero equals 1. "

Xerxes Excellent reply! Thank you. "In linear algebra, on the other hand, a field assigns to each and every point in some chosen space a value, generally scalar-, vector- or tensor-valued. Here relativistic effects do NOT apply to scalar fields." In this sentence you chose to use the words value, and that these values are assigned to a "point in chosen SPACE". So then if the space time continuum is "space", with the "value" being time, and it is relative. Then should not all "mathematical" fields represent this intrinsic property of "space" and "value" - time or otherwise" being relative. For example. If we allow that all numbers are defined as value and space, and that , that value or space is defined or undefined, infinite or finite, fractional or whole, positive or negative, then it is possible to show a relativistic relationship with all multiplication and division......that is your "functions" used in fields and rings. Naturally a redefining of numbers is necessary. So then all numbers are defined as being composites of Space and Value. Space being labeling of quantities of dimensions Value being labeling of quantities of existence other than dimensions If you will Xerxes you may take the following as an addition to all current field axioms. For every A in S there exist a Z1(space) and a Z2(value), such that any A in operation of multiplication and division is only representing Z1 or Z2 in any given equation. Naturally this axiom is tentative. I could pen it down further, but I will wait and see what happens here. Confused? You should be, Ive spent much time thinking about this idea of "relative mathematics" (maybe wasted).

Do they not exist not only as abstract toys for mathmaticans, but also as tools to describe our "space time" continuum and the realitys and interactions that exist therein. If the space time contiuumn is measured "relatively" speaking from a "perspective". Then should not operations that exist amongst elements and vectors in fields and rings also exist as relative to a perspective? If the idea of all field and rings and the study of infinity in these given fields and rings, is described as "successors and predecessors related by morphisms (functions)," then should not zero, existing as an "element" in fields and rings, not also posses a "successors and predecessors related by morphisms (functions)," so as to approach it on these "given" fields and rings?

Sato I took my defention for "set" from factual sources. Is the following definition wrong? "A set is a distinct collection of objects". Agreed I may be entrley misunderstanding this, but I am not disregarding them or makeing them up. I have not done a diservice to cantor or any others. Not by my recollection. In any case the box that is ment to hold the elements is not the set. It is the elements that are the set. Please copy and paste this "misrepesention" of notation that you claim I have made. I will try to rectify it. I don't recall useing any notation at all as of yet. But if you will.... The set of zero is {}. The "brackets" are not the set....the set is within the brackets....there is nothing in the brackets....therefore there is NO set. Lastly... if I did not really care about these "abstract" "nonprofit" "theoretical" ideas....then I would not be on this forum at all. You do me a disservice here. Thank you for your willingness to discuss this idea. Sato Upon investigation of your link..... "Set Theory is the true study of infinity".........Ha ha the very first sentence! Your sir or madam....can NOT approach zero on ANY number line by means of current number group definitions "real's, rationales, etc.".....therefore zero can not be a set of any kind! If zero is not a set then what is the nature of its space and value.......................?................. Side Note For AJB As the measure of space and time is relative to your perspective, so also is multiplication and division relative to your perspective.

If something (zero), is not a member of a set, and it IS the "set" of "emptiness"...........then there is NO set! Nothing is not the absence of something...because "it" or "nothing" doesn't exist.. There is no such thing as the absence of something. Zero therefore is NOT a set or an "empty" set......it is not a set at all....empty or otherwise. I do not use your point methods.....the "voting", or red and green "dust" is a little silly....I will however balance out all votes to zero where they actually belong until people like Studiot start throwing around the green pixie sugar. In any case no one other than Sato actually tried to give an opinion (on topic) here so TRULY thank you Sato.......lock this thread down boys and move on. Studiot If case 3 is what I am looking for, and then zero IS a member of the set...then zero is an element yes.....? So then if zero is an element then there MUST be something more to note on regards to the space and value contained in the element zero. Specifically how it "relates" to any other element in the set given.....so if yo don't want some red dust.......give an answer for the original question using your support from post 11.

Ajb I agree a more formal definition is needed, I shall not offer any so as to stay in "bounds". Sato Your just plain wrong. First off a set "please" verify, is defined as "any" collection of distinct objects....is zero an object then ? Is there more than one of them, so as to make a collection? Zero as a set does NOT fit the definition. Nor as you point out, does it contain any elements or any relations therein. All things required to be a set. If the "set" in question has no values or relationships, then there is not a "set" at all......by definition! Thanks Sato for you time. Studiot You will notice that Sato did not distinguish the difference between the space and value of the "set" of zero. Sato claimed that the space of zero was a relationship of it's elements. Therefore there is not a difference between the two, only that to define one, you must have and measure the other. Which I can agree with, but it shows then that clearly there IS NOT a difference between the two. It's merely a matter of a "relationship" of the elements involved.

I sincerly wish to only hear out others opnions. I have no desire to re-hash old topics of mine. With the moderators approval I ask the following, with out any intention of further reply. Is there a diffrence between the space of Zero and the value of Zero?

No objections....my apologies to the forum and pengkuan. To be fair....it was NOT off into the weeds it was right on topic....hijacking none the less I suppose. Again my apologies. No further comments.