1. ## Re: Relative Mathematics

Sets are just collections of elements [which may be a set].

It is the most basic building block of information [it contains attributes and a set is just a bunch of them].

If something is a piece of something then it is an element of a set.

Believe me - if you can't define the set then you can't define what you are trying to say in any specific or useful way.

2. ## Re: Relative Mathematics

Originally Posted by Conway
Dan

(z1,z2), are not members of any set...(they be considered pieces of the members of the set)

They are

z1=value
z2=space

"z1 and z2 for A, (any number) is "really" just the number given put into what appears to be an order pair"

z1,z2 for A = (A,A)
z1,z2 for x = (x,x)
z1,z2 for y = (y,y)
z1,z2 for 2 = (2,2)
z1,z2 for 3 = (3,3)

Any number has the same quantity of space, as it has value......except zero.

(_)= one ACTUAL space, no value = z2
(1)= one value, no space = z1

If I put these things together I get a number

(1) = 1

But if (2, 2) is what we would typically call the number "2" why all the extra work? Not counting the 0 stuff it would seem that you are just adding complexity where none is needed. You could simply say that the number 2 has the properties of space and value and not worry about the whole formalism. Is there ever a situation where we would have, say (2, 3)? What would that mean?

If you "think" you may be seeing what I am reaching for... I will continue....please let me know if otherwise... so that I may adhere to my aforementioned promise directly!
Listen, if there is ever a problem with your posts rest assured someone will mention it to you. Just go ahead and post and don't worry about any apologies.

-Dan

3. ## Re: Relative Mathematics

Chiro

In all fairness I know what a set is, I know what elements are. It is true that elements of a set are ALWAYS numbers? So then maybe you see the difficulty I am having. I am talking about pieces of numbers. Perhaps you missed that particular part where I was replying to Dan.....

(z1,z2), are not members of any set...(they may be considered pieces of the "members" of the set).....post #45

I am not aware of any set theory that currently "breaks" numbers up into their parts.....parts that are NOT numbers.

Dan

Understood.

"But if (2, 2) is what we would typically call the number "2" why all the extra work?"

Because in reality (2,2) as a representation of 2 is poor.

The reality is as follows

1

is composed of

(_) one quantity of space

as well as

(1) one quantity of value

if and only if I place the value into the space do I get a number

(1) = 1

This is imperative for reason relating ONLY to multiplication and divison....so as you said forgetting zero.....

2 x 3

The above expression does not have "numbers", they are z1 and z2, I may label either symbol as value or space....(commutative property)

so that....

2(as value,z1) x 3(as space,z2).......yields the following action

I take three spaces.....
(_,_,_)

I take the value of two.....
(2)

I put the value into the spaces and then add

(2+2+2)=6

or

3(as value,z1) x 2(as space,z2)........yields the following actions

(_,_) I take two spaces

(3) I take the value of three

I put the value into the space and then add

(3+3)=6

4. ## Re: Relative Mathematics

[QUOTE=Conway;911867]It is true that elements of a set are ALWAYS numbers?´/quote]
No. The set of all Disney elephants contains Dumbo, some other elephants, and no numbers.

Originally Posted by Conway
I am talking about pieces of numbers... I am not aware of any set theory that currently "breaks" numbers up into their parts.....parts that are NOT numbers.
Your parts are, mathematically, numbers. You might want them to represent something else, but unless you introduce some rules to the contrary, they appear to function exactly as numbers.

What you have thus far described (not in these terms exactly, although you were closing in on it) is that you have a set of ordered pairs $\displaystyle (z_1,z_2) \in \mathbb N \times \mathbb N$. You call $\displaystyle z_1$ the "space" and $\displaystyle z_2$ the "value" (although these terms mean nothing mathematically: their behaviour is defined by other statements). You all have implicitly defined a bijection $\displaystyle \mathbb N \times \mathbb N \mapsto \mathbb N$ defined by $\displaystyle (a,a) \mapsto a$.

That's all well and good, but very thin. What happens next needs some formalisation. It reads as a very ad hoc construction that looks unlikely to stand up to any rigorous interrogation. You say that, for multiplication $\displaystyle (a,a) \times (b,b) = (a, ab)$: taking the space from $\displaystyle (a,a)$ and then putting $\displaystyle a$ copies of value $\displaystyle b$ into those spaces. (I note here that you have absolutely used the fact that both the space and the value are functioning exactly as numbers). However, as noted before, we now have something that isn't in the definition of the set. You also claim that we have a map $\displaystyle (a,ab) \mapsto ab$ which stops the mapping from being a bijection because we have $\displaystyle (ab,ab) \mapsto ab$ already. Essentially, we seem to be heading to a place where the "space" is completely immaterial to the mapping. You have also stated that, due to commutativity of multiplication we have $\displaystyle (b,b) \times (a,a) = (b, ab)$ and that this also maps $\displaystyle (b,ab) \mapsto b$ further damaging the bijection idea and further illustrating that (up to now) the "space" is irrelevant.

None of this stops you from continuing to define this system, although it does make me question the point to it all.

5. ## Re: Relative Mathematics

Archie

Excellent post!

Lol...your statement regarding elephants was NOT fare....though entirely accurate........

If 1 = elephant.....then elephant is a number...........What are the pieces of an elephant?.....

It's "dimensions" , or space....

It's "being", or value.....

neither of which are described as elements in the set......

Do you at least see my point here....

I have withdrawn my claims on mapping .....as I do NOT believe it is possible....or applicable....as I pointed out in a reply on mapping that came directly from Chiro.

quote
(I note here that you have absolutely used the fact that both the space and the value are functioning exactly as numbers).

I have expressed fiercely the exact opposite.(except when combined) It is impossible to separate space and value phisically...it can only be done abstractly......hence my attempt to do so with "symbolic numbers"

If you will....

Let's set aside all set theory
Let's set aside all expressions involving zero

Do you think/agree the following makes sense....

1

is composed of

(_) one quantity of space (sometimes large or small)

as well as

(1) one quantity of value (sometimes elephant or 1)

if and only if I place the value into the space do I get a number

(1) = 1

If you Archie, Chiro, Dan do not find the above to be logical...

Then I yield here and now....

6. ## Re: Relative Mathematics

Originally Posted by Conway
Do you think/agree the following makes sense....
Not in the slightest.

That's not to say that you couldn't build up a system based on the idea.

In a set of elephants, you can happily consider each elephant to be a collection of components, but for that to make sense you must define what those components do and how they interact with other components of the same and of different elephants. I don't see the components of an elephant as "space" and "value" at all. Trunk, legs, ears, etc. yes. Some ill-defined idea of "space" and "value", not at all. But that doesn't mean the idea couldn't be made to work in some context.

We can talk about chemical elements and how they react with each other, or we can talk about molecular structure - but only if we determine how the nuclei and electrons interact.

Your problem is that you are too wedded to your concepts and terminology. What you are calling a "number" isn't a number. It's a collection of elements (which may or may not be convenient to represent as an ordered pair of numbers). The problem everyone else has is that you make little attempt to formalise your ideas, instead preferring to wander off on a stream of imprecise language. It doesn't mean anything to anyone because the concepts aren't clearly defined and there's no earthly reason that anyone else can see why you should be using them or what they actually represent.

7. ## Re: Relative Mathematics

Sets don't have to contain numbers - they can be anything.

They can have any structure so long as when you take intersections and unions they are consistent.

You have to determine how to break things up and then represent them as a set.

Numbers are just things that make sense geometrically and with arithmetic - the information represented doesn't have to be a number.

If you have a so called "piece" of a number then you have to decide how to break up the number.

You can represent that in a set but you need to determine the structure of how to break up these "pieces" by defining what elements the set has.

8. ## Re: Relative Mathematics

Chiro

Fine....again lets set aside any talk of SETs at this point.....as in the op I never mentioned sets of any kind. I truly have only meant to deal with arithmetic. If you wish to talk of that... and we can come to terms, then maybe WE can find a way to apply it to sets....which is what I was trying to do with Dan.

Do you think/agree the following makes sense....

1

is composed of

(_) one quantity of space (
as well as

(1) one quantity of value

if and only if I place the value into the space do I get a number

(1) = 1

Archie

I offered formal definitions for both space and value in the original post. Apparently you did not read it.
I offered formal definitions for the combining of space and value in the original post. Apparently you did not read it.

This is why you think that I have "wondered off"...because you NEVER read the original post.

I have FORMALIZED, PERCISE, definitions for both! And have been attempting to explain those ideas in as many other ways as possible...thinking you had actually read them.

Shall I continue.....if so....just for you Archie my friend....I will give these exact definitions and operations again....?

Space = labeling of quantities of dimensions.............see VERY precise
Value = labeling of quantities of existence other than dimensions..................see VERY precise

IT is in multiplication that the value given is placed into the space given, then all values are added............again very precise
It is in division that the value given is subtracted equally into the space given, than all values are subtracted except one.......and again very precise

9. ## Re: Relative Mathematics

To All,

I think I have taken this thread as far as it can go at this time....again....lol.

Therefore I yield in defeat to Dan, Chiro and Archie

Thank you all.......

I will return to my studies in hopes of maturing these ideas. Maybe in another year I will return again.

After all the third time is the charm!

Sincerest gratitude to all!

10. ## Re: Relative Mathematics

Originally Posted by Conway
Space = labeling of quantities of dimensions.............see VERY precise
Value = labeling of quantities of existence other than dimensions..................see VERY precise
Those are not mathematical definitions. They are the interpretations that you wish to apply. As it is, I don't think those definitions do make much sense in many arenas. Elephants constantly change the "space" they occupy and their value is not obvious. All numbers, to me, have no "space" that they occupy, so in mathematics I see no point in recording the fact.

I didn't read the OP in detail. It was too long and dense, and I've read previous versions.

But, as I've said before, just because I don't follow your thinking doesn't mean that you have to stop. But for it to make any sense in mathematics you must find a precise mathematical description of what you are doing.

11. ## Re: Relative Mathematics

In my opinion they aren't anywhere near as formal as you think they are.

If they were then people wouldn't have problems understanding you - but they clearly do based on the replies you are getting.

It should be simple for you to answer the questions posed but you don't.

Also - when you use things like numbers and non-numeric objects in combination then they are just sets.

It also doesn't matter if you combine things with arithmetic or something else - you can use sets to do many things.

Like Archie said above - they aren't mathematical definitions and you might as well be a type-writing monkey because the stuff you are writing doesn't make much sense at all.

12. ## Re: Relative Mathematics

Originally Posted by Conway
Therefore I yield in defeat to Dan, Chiro and Archie
It's already been said but it bears repeating. There is no defeat here. No one has any problem with you it's just that your arguments are not well formed. What's happening here is a learning process. There's no shame to that.

-Dan

13. ## Re: Relative Mathematics

topsquark:

I understand that bringing this up like this might bring on a ban. I do so at great risk. I had hoped you might re-read this thread. Then compare it to my recent previous behavior on other forums. I accept responsibility for my clearly inappropriate behavior. I treated romesk especially so. For this I am sorry. But I have struggled from the beginning to be polite and do my best to learn and make progress. Have I not done so? But I have been severely abused by some here and others elsewhere. This takes its toll. I would hope you would also consider the context of all the versions I have posted here over the past few years.

Again I apologize to all of those I treated poorly.

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