# 0, 1, infinite model, question

1. Apr 11, 2005

### Moonrat

Hello. I was hoping someone here can give me a pointer or a link..

I am not a mathematician, or even in a math course, but I
am doing research regarding a dialectic that refrences the numbers 0, 1, and 2 in it's conceptual environment.

I was having a discourse in my research with a former math professor from Princeton about how it works, and he informed me that the numbers 0 (mystery), 1(true) and 2 (false) how they are used in the dialectic (as basic distinction of idea) is called in mathematics 0, 1 and 'infinite'. refrencing the three basic distinctions of number... Is that a higher math, a specific branch? What is that called? I am wishing to write about this and cant find any source or even where to look. Any help would be great in this regard.

MR

2. Apr 11, 2005

### HallsofIvy

Sorry, but it looks to me like this has nothing to do with mathematics. As far as I can see you are only using "0", "1", and "2" as labels and could as easily use "a", "b", "c".

"0, 1 and 'infinite'. refrencing the three basic distinctions of number... " is just nonsense.

3. Apr 11, 2005

### Moonrat

mmm, thanks, I guess..however, it's not nonsense, and it's not like quanitfying things down into a, b, c at all, that was a bit of an assumption on your part. This was a former math professor at Princeton whom informed me of this, so I think he would have an idea about what he was talking about. perhaps it is a refrence in a branch of math you do not yet understand....

using common language, it can be explained simply that there are three basic distinctions to number.

0 is the value for number with an unknown or non value. 1 is the value of a finite basic unit , and 2 , or 3, or 4, ad infinitum, etc etc is merely an arrangment of '1's.

3, count them, three distinctions.

I dont have the mathematical languages to explain this, but I do know it is a princaple, and a mathematical one....

MR

4. Apr 11, 2005

### matt grime

Just because an ex=professor explained something to you doesn't mean he understood what you were asking, and more likely that you didn't understand what he was getting at.

One interpretation might be this:

take 0, the algebraically we obtain no more elements.

so we add 1, which is the multiplicative identity, then algebraically we can get more things, but we never obtain anything *algebraically* that we think of as infinite.
Perhaps. But only that professor knows what he meant. We do not, as this isn't mathematics ion the sense of a universally agreed convention but his personal philosophy about something.

5. Apr 11, 2005

### Moonrat

matt, thank you for your time and response,

hear me out a bit, please...I have been developing a dialectic for the past two years, and am just now getting to working through some of the complex math aspects, which is not my forte, I admit...

yes, I agree, that may be true, however, what may also be true is that he understood me, I understood him, but you do not understand us. And that certainly is not your fault, but mine. So, I have to explain this feature as best I can, rationally, using common language. However, this is a distinction that is found in number, and you just pointed it out.

yes, and this I would explain, in my common language, that this is a 'non-value'.

yes, we add 1.Or, from 0 we obtain 1. One, in the dialectical sense, is simply 'distinction'. Now, I dont know how 'distinction' is refrenced in mathematics, but each thing that can be distinguished is always '1' thing. Now, there is one, and then there is what happens to 1 when multiplied, divided, and sumed.

It becomes a multiplicable identity because of the 'infinte' number of possible combinations of multiplying 1.

yes, agreed. but we do have an infinite number of possible combinations, and that is the point of the infinite environment. Each one of those combinations is assigned a number, any number, but 1.

So, to put it poetically, we can say that mathematics is then the 'play', of 0, 1, and infinite. 3 distinct mathematical environments that all numbers decontruct into...

hmm, ok, I can see that perhaps, but to me, he did say 'Ahhh, I see what you mean now, and in mathematics, we call that 0, 1, infinite....( i dont know if it would be parsed that way, written, but those were his exact 'words' to me)

Are you suggesting that this is merely 'philosophy of mathematics' or something?

the dialectic distinquishes this relationship, found in math, found also in perception, and in logic creates a ternary system of true, false, and mystery as a gaming dynamic inside of a dialectic.

Now, I just want to understand that relationship in math so I can understand it clearer inside of the dialectic, so I would love to keep this discussion moving forward.

Thank you once again.

MR

Last edited: Apr 11, 2005
6. Apr 11, 2005

### HallsofIvy

What you are talking about is NOT mathematics.

7. Apr 11, 2005

### Moonrat

hmm, puzzling. I ask one mathematician, one whom was rather highly valued and with respectful published work, and he says, yes, this is mathematical, and you say no...interesting...

So to understand you clearly, there is NO mention, parsing, noting, or perception in all the annals of mathematics that simply distinguishes the basic ternary interplay of number?

Surely mathematicians have noted this perception in number before....are you suggesting this is philosophical and not mathematical?

How so? If it can be quantified, how so is it not mathematical, can you explain? Do not all 'normal' numbers fall into either of those three categories? And if it is not mathematical, then how is it the nice fellow who posted after you noted the algebraic relationships immediatly?

MR

Last edited: Apr 11, 2005
8. Apr 12, 2005

### matt grime

You certainly sound like a philosopher.

There is, as far asI am aware nothing that states "in mathematics there are 3 kinds of ... 0, 1, and infinite". Though some mathematicians may draw an anaolgy.

Hurkyl, is right, though, this isn't mathematics, as in "something done by a mathematician", more precisely what you're writing about is n't mathematical:

You say something about an infinite number of combinations making 1 the multiplicalbe idetnitty. this isn't meaningful to a mathematician. Also, we cannot speculate as to what "non-value" means to you. I do not see how *you* have obtained 1 from 0.

And I do not know what you mean by numbers deconstructing into 0,1, infinite.

however, relatign them to true false and mystery is speculative to say the leas. Assiginin 0 and 1 to false and true is boolean logic, nothing more. mystery is a mystery.

9. Apr 12, 2005

### Moonrat

Matt,

hey, be careful, those are fighting words ;-)

ok. but the analogy is mathematical. i.e it is a rational observation or perception of number, yes?

Well, yes, that I agree with and see. However, what I am refrencing is also found in mathematical 'perception', or what I am calling 'the perceptional environment of number'. It's not like i am talking metaphysics here or anything of the sort. Just simple observation.

Sorry, that was me 'attempting' to make it meaningful to a mathematician. Actually, that is not really meaningful to me either. I was trying to parse what i am signifying into a lanuage you can understand...and am failing miserably thus far, but perhaps you nice intelligent fellows will allow me a few more rounds...

Here it is practicaly. I have no money. 0 Dollars. I get a job. Now I have 1 dollar that the job pays me. Before, my monetary value was 0, now it is 1. the 'philosophy' would be that having 0, or nothing, or non-value, inspired me to 'get up off my ass and get a job' so I could obtain the 1.

Or, mathematically, I am looking at a number line with 0 in the middle, and I can count, in an infinite number of directions, 1's coming from the 0 and spanning out, both positivly and negativly. 0,1,2, 3..etc

Not being a mathematician, I can only speak for 'linear numbers and number lines'. I am sure there are qualities of number that I am simply unaware of that can express marvelous vectors and all sorts of things. The math professor I met with was fascinated a bit with the dialectic, and he said I may be tapping into mathematics used in quantum computing. Which is real neato to say, but hopeless for me to understand in relationship to anything.

So, let me know if this makes sense to you. Numbers are symbols, yes? They are symbols that represent, like a language, quantative units. Are we in agreement in my poor man's mathematical language thus far? In this sense, there are three qualities of what numbers express, summed up simply as 0, 1, and 2. Let me explain the 0 here so you can come to see what I mean by 'non-value'.

0 in math, historically as I am sure you are aware of, has presented troubling notions for mathematicians in the past. In my common speak, I am simply observing that 0 is a number that is a numerical value for that which has either no known value or an unknown value. I mean value in the sense of that which can be quantified into a unit. Thus, on a number line, what I mean is simply expressed as 0, 1, 2, 3 etc etc. We 'begin' with 'nothing' and that 'nothing' we signify with only 1 number, 0.

There is no number that holds this value in linear mathematics other than the number 0. In the dialectic, we place this same value onto perception and idea as 'mystery'. Mystery, as defined in the dialectic, is simply an idea, proposition, or perception where you cannot distinguish yet what is true, from what is false. You could say that to me, much of mathematics is 'mystery', and as you can see especially in this instance, i have one mathematician telling me one thing, and another mathematician another thing. I cannot yet deduce the 'true' value of this yet, it is suspended in 'mystery'.

0 is to number what mystery is to perception of true and false.

Ok, so how then would 1 be true in perception or idea? Simple. All numbers, in the linear sense, are simply combinations of 1, like we have already mentioned. 1 is the number of 'unit'. A unit is always refrenced as 1. 1, or a combination of 1's, either postivly or negativly, is what we are left with when we decontruct all numbers into thier basic 'units'. 1,000, 000 is just a 'million' 1's. A 'million' units. So in this sense, 1 is the only 'true' number, and all numbers are simply 'expressing combinations' of 1.

Thus 2 is the first pure 'false' number. It is false in the sense that it is merely in service to expressing a number of combining 'truths' or 1's. The 'ding an sich', what we call the 'thing in and of itself', of 2, is two 1's. The ding an sich of 1 is 1. We could say 3, 4, etc etc is false in the same sense, however, 2 is the first pure expression of this quality in linear numbers, and philosophically it elucidates with more subtle princaples that are irrelevant to discuss now.

This is not speculative, it is observational. In the dialectic, 'false' is a quality of absense of truth in decontructed form, yet it points to truth in combination or expressive form.

Thus, we have three distinctions or values of 'truth' for number, perception, and idea.

0=Mystery or Mysterious Idea
1= True or Objective, rational Idea
2=False or Subjective and artistic idea.

I am not qaulified to mathematically advance this concept, that will be someone else's job. But I am qaulified enought to hammer out the basics. I have been developing this for over two years, and am pretty clear about these functions and how the apply, and I also can make them work when I apply them. The trick for me now is understanding how they read to mathematicians.

yes, that I am aware of. However, although many have drawn similarities to Boolian concepts, this is not boolian. It's another language, and indeed, if correct, and it appears thus far that this is correct, it is a 'natural' mathematical or rational perception language basic to human being.

matt, thank you for your time.I would appreciate if we kept this going a bit. I still have plenty of work to do, but your really helping me thus far.

Glad to see that the mathematicians are horrible at spelling just like the filosophers;-) :yuck:

MR

10. Apr 12, 2005

### matt grime

if that's what you think "mathematical means" that is.

But there is nothing mathematical about that; 0 has not created 1; you have creted symbols to express something; in mathematics 1 predates 0. Perhaps I should explain that in mathematics generally things are mathematically constructed from other things. For instance one constructs the integers from the naturals, then one makes the rationals, reals, complexes and so on.

but nothing here "makes" you construct 1 from 0.

presuming by this you mean the natural numbers. no, this is backwards to this mathematician. mathematical objects are used to describe things in the real world. they can be used to accurately describe (some) quantities, and this is quantitative thing is the origin of some part of our study. one model for the natural numbers is by, say, finite set cardinals. but it is all a matter of opinion: some will call me a formalist for this opinion in a derogatory manner.

no. define it.

no, this isnt' true: if the temperature of the water is 0 degrees C I know exactly what that temperature is.

there is no number that holds the value 2 apart from 2 as well. so?

mathematically, 0 is the additive identity, 1 is the multiplicative identity.

it's not suspended in mystery, just undefined unmathematical terms.

not until you define what a combination is, because you've yet to do so.

the same observation still holds. and all you're saying is the N is generated by 1 under addition. this is not a mystery.

this is an odd use of the word false. usually two truths make a truth.

i think i'd prefer the words irreducible and reducible

this contains a lot of non-mathematics that mathematicians won't care about.

my spelling is almost flawless; i continually obtain 100% in such tests. however my typing is abysmal.

11. Apr 12, 2005

### arildno

Well, I'll give you one concession, moonrat:
The conceptions of "no thing", "the unit/basic amount of finiteness" and "boundlessness/infinite" are certainly ideas about quantity which ordinary people have vacillated back and forth between through history.
What you seem to be missing, however, is that these extremely imprecise ideas (which, hence, enable their users to embark on flights of fancy) have practically no relevance to actual mathematics.
Hence, you should rather try to see if you can utilize your distinction in a sort of history of mentalities; to think these ideas have any deep relation to mathematics as such, is simply to bury yourself in a dead-end.

While, conceivably, your tertiary distinction might be an interesting classifying tool for the shifting, internal dynamics in numerology as evidenced in its history, dragging them onto mathematics proper is simply a misapplication of the tool.

For example, the distinguishing tool is not really able to clarify the close resemblance of 1 and 0, in that they are both identity elements for distinct binary operations.
Furthermore, the "no thing" concept is not really a good way in understanding how "0" appears as a reference level, in some uses of maths.

Last edited: Apr 12, 2005
12. Apr 12, 2005

### honestrosewater

As they are usually defined, numbers are not symbols; Numbers are what the symbols represent. Numbers, as all mathematical objects, are usually also considered to be abstract objects.
You just "quantified" it when you said you had 0 dollars.

Last edited: Apr 12, 2005
13. Apr 12, 2005

### Moonrat

Matt

well, like I mentioned in my previous post, much of mathematics is 'mystery' to me. However, I do assume that when I can quantify something, that the process of 'quantifying' itself is mathematical. Any quality of 'adding, dividing, or multiplying' I would assume would be mathematical, or would be able to be parsed into a mathematical langauge. Are you suggesting that I am mistaken in this?

hmm, it appears to me that here we are having perceptional snafus. I of course do not mean that '0 creates 1' in the same sense that I can create a work of art, or, for example, in a few months I am expecting a son, so I dont say that I and the mother created a child in the sense that 0 creates 1, that would be absurd and irrational.

I simply mean that, from a specific POV, we can say that it appears that from 0 comes 1. We can distinguish nothing from one thing, and when we distinguish 'nothing' mathematically, we give it a 0. When we approach this with a linear P.O.V., then we count..0, 1, 2...right? I am only refrencing this simple component, nothing more or nothing more complex than that.

Here I disagree. I have not created any symbol. I have merely noted that perceptional values (true, false, or mystery) to indeed 'true to numbers', and indeed true to those numbers assigned specifically. It is a basic perceptional unit that is found in all language, including mathematical language, or rather that is my arguement.

and yes, in terms of history, i do agree and see that 1 predates 0, however, that is not my point, historical record is not how they relate to each other.

Ok, I can follow that.

agreed.

and ok, now i see a bit more...and this is interesting to me what you write below...

Okay, now this is where it gets interesting for me. This opinion you proscribe is a 'quality of perception', not a 'mathematical 'p.o.v.'. but a 'p.o.v. of mathematics'.

this quality of perception is defined as 2, false. Notice how you mentioned there is more than one way to view this issue in mathematics. I would imagine that although each mathematician would appear to have a sound arguement regarding how he arrives at his 'opinion about mathematics', there is no 'sound way to determine' which mathimatical perception is empirically true. Yet all mathematicians would agree about the numbers being viewed, just not the relationships that they have.

This is what the dialectic of 0, 1, and 2 defines, the perceptional p.o.v.

Please dont expect me to parse things into a language I dont understand, that would not be fair. However, I can define mystery as it is defined in the dialectic.

0 = mystery, an idea that is both true and false at once. It cannot be determined, defined, or percieved any value in relationship to it's linear or extending environment.

For example, you mention that

. It has 'no celcius value', as opposed to 1 degree C, 2 degree C, etc etc..

0 degrees suggests a centering value in relationship to 1 degree C, etc etc, it's a POV. Without the POV, there is no distinction between the levels of temperature at all, and we could not have -1 degree celcius either without the 0. It's value is relational. Like I said, 0 apears is either 'non, unestablishing, or unknown' value.

the value of 2 is 1 and 1. the value of 1 is 1. the value of 3 is 1 and 1 and 1. All numbers relate to 1.

2 IS 1, 1. again, this is a relationship of perception. 2 is a refrence for two 1's.

what do you mean by 'additive identity'? I understand multiplicative identity, but what does it mean that 0 is additive? does it mean that it is the number that we can only add to, and not subtract from? In this sense, yes, I can see that.

And if so, then what I am refrencing would agree that 0 is the additive indentity, 1 is the multiplicative identity, and 2 through infinity are how many combinations identity is expressed or parsed.

that is the same thing in relationship, just expressed with two distinct qualities of perception.

ahhh! now this is where I run into trouble...allot. here I run into trouble because I understand that there is a 'method' to parsing, so to speak, that I may be completly and perceptionally unaware of. The best I can do is describe what I mean by 'combining' in common speak, and then request you try to see what I mean intuitivly at first, and then rationally parse afterwards..

So, to me, mathematical combination would be adding, dividing, and multiplying. I mean combination in the same sense as this.

There may be much more to combination than what I describe here in mathematics that I am totally unaware of.

yes, I agree. Nor was I suggesting it was mystery. So I dont understand your rebuttal here. Here we are not even in conflict.

yes, I agree and can see that it is 'odd'. however, in relationship, it is accurate. This is a rather tricky aspect of the dialectic to percieve at first. It is how it 'uses' false as another function of truth.

I am sure I am going to ruffle many a feather when I suggest this, but herin lay the three perceptional distincions of truth. For now, we can simply agree that 'truth' is merely that which holds observable function.

1=pure truth. a=a. ( it's function as true is objective.)
2= false truth. a=b. metaphor. opinion. (it's function as true is purely subjective)
0=mysterious truth. it is undetermined, unknown what value of truth can be obtained from it, other than it is true that we cannot determine finite value.

that is fine, as long as we agree that we are refrencing the same function. I can simply say that all (whole?) numbers are reducible to 1. 1 is reducible to an finite number of .1's. 1 defines the relationship of the 'finite'. finite is reducible to 1. any finite number is reducible to 1. there are an infinite number of 1's, thus, an infinite number of combinations of finites.

I agree that I am describing this descriptivly, yes, using a distinguishable language, but we are on the same page here.

Now, if you dont mind, let me show you what I mean by 'parsing' perception into these relationships. What you wrote above was a false idea.

However, I can see what you mean from your POV, and from your POV, I can translate it away from an opinion, subjective, into an objective statement. "So far, what it appears you have presented to me is not something that is applied in mathematics"

And yes, I agree. however, I am not wishing to introduce a new mathematical proof, I am wishing to show where this perception exists in mathematics in relationship to mathematics, and then I am requesting you help me find how this can be expressed into mathematical language.

If something has a pattern, it can have a mathematical expression, no?

yeah, that's what us filosophers say too;-)

Thanks Matt, I really appreciate your time.

MR

14. Apr 12, 2005

### Moonrat

yes, agreed. we are refrencing the same thing, just explaining it differently

yes, I know, however, I quantified it as having non value. 0 is value for no value.it is only a unit from the POV of numbers, it is a 'unit' which contains no value, as opposed to 1, which is a unit that expressed the value for unit.

Thanks for keeping your eye out.

MR

15. Apr 12, 2005

### matt grime

The choice of 0 as the freezinv point of water is completely arbitrary, as the other scales of temperature indicate.

0 does not necesarily indicate an absence of something. This is where you need to separate mathematical objects, such as the ste of natural numbers, from their uses.

You've still not explained what you mean by "combinations".

To give you some idea of the oddities in mathematical philosophy how about

www.dpmms.cam.ac.uk/~wtg10/reals.html

Your decision to assign 0,1, 2 or infinity to some other context is not something I encourage. It has led to some awful things in the social sciences. One needs only recall the Sokal episode. Also your assignment is completely aribtrary and says more about you than either mathematics or philosophy, but then that is possibly true of any stance one takes about a philosophical argument.

Incidentally 0 is an (the) additive identity since 0+x=x for all x, just as 1*y=y for all y.

Yes, all natural numbers are *by definitoin* just those things that can be obtained from adding 1 to itself repeatedly.

However it is then that we define 0 from 1, if we are of the desire that 0 is not in our natural numbers. Some people declare 0 to be the smallest element of N.

From these we can by adding in all the "combinations" in your sense, only obtain the rational numbers. There are numbers that cannot be described from these things, such as root 2, e, pi. See that link.

But this is different from applying it to some quantifiable thing.

This is jsut a reply "for now" not a complete reply. I will try and write more later

16. Apr 12, 2005

### Moonrat

yes, that too is my point.

i would say that 0 necessitates the absence of 1 by default, no? That is all I am suggesting. Again, this is not a metaphysical discussion, although I can see how it may be percieved as such

the function of numbers is true in all environments, I would imagine. I would imagine both conceptually and imaginitavly that 0 or nothing always and permanently suggests the absense of 1 or a thing.

I have the best I know how. perhaps this is something you can help me with. Can you intuitivly see what I mean first? Combining, to me, is simply 'adding, multiplying, or dividing' of objects (1's) with other objects (1's). I am not sure what I am being unclear here on, as I am refrencing simply that and nothing more.

ahh, now that's a link. thanks so much for that. Will study it soon.

hmm, let me look into that.

it depends if the ideas are true or not in the objective sense, right? Believe it or not, I am not wishing to develop a philosophy, nor is this about philosophy in my eyes at least either. This is about perception, and how perception relates to how we view or value information, be it mathematical or otherwise.

yes, we are on the same page.

hmm, i am not sure if I follow, are you saying that some suggest 0 is a natural number, and some suggest that it is not a natural number?

If is not a natural number, then what qualitive of number is it?

yes. So my model is refrencing natural and rational numbers, and is true in that sense?

Would this proposition be true then? 0 is to mystery what 1 is to true what 2 is to false in perception and in rational and natural numbers.

how so? this is a quantifiable thing in perception. It is basic to human perception.

thanks, looking forward

MR

17. Apr 12, 2005

### Moonrat

Sokal

matt,

By the way, I just freshened up on Alan Sokal's 'hoax', and I must say, it is similar, but not in the way you suspect. What he did was an example of what I refrence as the 'political approach' and showed how perception can percieve a false truth and confuse it's function as a pure truth. I dont know Sokals reasons for doing this, but what he exposed is a perceptional snafu that this dialectic of perception addresses and decontructs. But that is beyond the scope of what this discussion is refrencing, but thanks for the great link..

MR

18. Apr 12, 2005

### honestrosewater

What does it mean to quantify something and for something to have a value and for something to have a non-value? Value, amount, quantity, magnitude etc. are all closely related if not synonymous, so you'd have to clarify how something can be "quantified as having non-value".
I don't understand this. It seems to mean "0 is the value of x if and only if x has no value", but that's a blatant contradiction.
What is the distinction between a unit and a number? From "the value for unit", I gather all units have the same value. In that case, neither 0 nor 1 is "a unit from the POV of numbers", because from the POV of numbers, 0 and 1 have different values.

19. Apr 12, 2005

### Moonrat

Hmm, I like those questions. I am going to get a bit dangerous here and open up some territory I am still understanding myself, but In common language I would respond that when we quantify something, it means we identify either number or measurement into mutual language or symbol referencing a distinguishable unit. For example, I can distinguish 1 glass of water, and then the amount of water in it, and then add a value for the total volume, etc etc.

From the POV of perception, we can then say that all things that can be distinguished can be assigned a value appropriate.

Value in the objective sense that I reference would mean it's equivalent in relationship to other objects. the value of 1 being a finite can only be in reference to an infinite or at least a continuous set. thus, we assign that which has no finite value, 0, to help define the finite value, 1, and vice versa.

are you saying that I would have to have an objective criteria for what quantifies something not having a finite value?

0 is the absence of a finite value. Where ever there is a signifier for that which is the absence of a finite value would be synonymous with 0. Having that defined, we can then distinguish the finite value (1) with ease..

hmm, no more so than 0 in general, I would imagine. You act as if I am introducing the concept of 0 into mathematics for the first time! 0 is a paradox a bit after all. I even think Aristotle, or perhaps his cult, feared the number and even had murdered the Greek mathematician who suggested it's existence and what it did to their system of mathematics.

remember, 0 is non value in relationship to the natural numbers that are counted from it.

hmm, I have written a response for this, but I just deleted it. this is a wonderful question. I may need a bit of time to think about this answer, but for now, let me say that to me it appears as if a unit is a finite, functioning in relationship to other finites, and any whole rational number would be simply a collection of finites or units or that which can be distinguished or quantified into units. A unit is the deconstructed finite that appears when we make basic distinction.

Or, you could say that the basic unit of number is 1.

and then to add even a bigger mess, we could then say that all finites are abstractions or conceptual objects or 1's, but that is probably getting too philosophical here.

YES!!! Now here is where it gets rather delicate since we are overlapping two environments confusing them as one, and I can accept that my explanations are a bit faulty or needing some help, but 0 and 1 have different values in relationship only to each other. 0 is no sum, and 1 is finite sum. However, from the pov of number, 0 is a unit, 1 is a unit, 2 is a unit in the sense that they are are distinguishable from each other, each one a 'unit of or measurement of number', 0 being the 'number' for non value, the 'unit' for 'no unit'.

perhaps with all of this confusion about 0, you can see that 0 being an idea that is 'both true and false at once' may seem a bit apropos here.

Good questions, and you got me really thinking....it's a treat to receive such rational questioning, thank you so much

MR

Last edited: Apr 12, 2005
20. Apr 13, 2005

### matt grime

I can't make that make sense mathematically.

Is not 2 the absence of 3? Are you talking of the zero element in Z, Q, R C, or some other field or ring? Do you think that the 0 elements of all rings are equal?

I think you're talking about an application of some numbers, to be honest, and not about any of the inherent mathematical properties of the numbers.

what does it mean fo a function to be true?

i am suggeting that. you find that odd because you think that the name we give to something is somehow intrinsic. there are lots of mthematical objects/concepts that are different and have the same name.

what sense of true is this?

not in mathematics.

Last edited: Apr 13, 2005
21. Apr 13, 2005

### Moonrat

Matt

Again, thank you for your time and keeping this discussion going with me. I hope you realize what an assistance your being.

I think I may have a false idea about what mathematics ‘is’, this may be true. I assume that it is a rational language that assigns mutually agreeable symbols to observable functions, and measurements. I want to come to understand what mathematics is then in the pure sense. I want to see what you see.

I said: I would say that 0 necessitates the absence of 1 by default, no?

Hmm..puzzling that you cant see this, and your ‘reason’ is…

Yes, 2 is the absence of 3, but it is NOT the absence of 1, it is the inclusion of 1. All numbers, at least the real and the rational, are the inclusions of 1 except for 0. I am merely making an observation about this number.

In relationship to all other numbers, be they real, rational, or natural, is not 0 then the only number that holds this value? It permanently suggests that ‘1’ is as ‘nada’ as the boogie man and Bigfoot. Where there is 0, no 1 can exist…

I really wish I knew the answer to that question, however…when you ask….

I think I see your point. In relationship to what they may signify individually on each ring, no, but in relationship to 1, yes.

I think what I am having difficulty explaining here is the fact that I am only referencing 0 in relationship to 1 and 1 in relationship to 2, and that is it. I am going no further than that, I cant, I am not a mathematician!

I can assure you that I am only referencing this relationship, and I understand what your telling me, your saying that although this relationship between numbers may be perceived to exist, it is not utilized or acknowledged, even needed, in all of mathematics that you are aware of.

Is that what you are telling me?

Well, yes and no. I am talking about, for sure, inherent properties in the numbers 0, 1, and 2. Your telling me, and I can accept this if you can continue to argue this as true with me rationally, that what I am observing is not a mathematical function.

The question I am asking now is, if what your saying is true, how is it that these inherent properties of number that I am able to observe and define not mathematical, and how so?

a function itself is true by default how I define function and truth. If a function is not ‘true’, then it is an irrational or imaginary conceptual object that is still has function, just not the function it is signifying. Once something has an observable ‘function’, (let me define function as ‘relationship’ to other objects or 1’s to other 1’s), it’s ‘true’ in the objective sense. A simple common way would be to describe function as an object’s ‘cause and effect’, it is not just conceptual, it is observably physical, and can be broken down and dissected and communicated intoa conceptual formula…this is ’physicalism’, no?….(and now we are getting off topic and I am most likely confusing the issue here, so if non of this makes sense, let's move on!)

so to be clear, your saying 0 is not a natural number, and therefore by default has no ‘intrinsic quality’ that can be quantified? Or it can be a natural number or even reference a natural, depending upon how it is defined in a formula?

And if so, that 0 is permanently not a natural number, then I am saying that yes, if this is true, then 0 is the integer that represents the absence of natural number.

I am not trying to find what I am defining in math, but rather the math in what I am defining. I assume that if something has an observable pattern, it can be quantified, am I mistaken in this?

Thank you once again

MR

22. Apr 13, 2005

### matt grime

good, cos that is how mathematics works - simply by deducing things from the rules.

.

to be honest, as soon as i read that i switch off, as will almost any matheamtician. in what sense are you using irrational or imaginary? the mathematical one?

so to be clear, your saying 0 is not a natural number, and therefore by default has no ‘intrinsic quality’ that can be quantified? Or it can be a natural number or even reference a natural, depending upon how it is defined in a formula?

some people declare that the set of naturals contains zero, some do not. I am abivalent and use which ever is more convenient.

you need to define "absence"

as it is all you appear to be doing is stating

"I want 1 to be the smallest natural, i will declare that the other naturals are combinations of 1, and i will assign the phrase "indicates an absence of" to say "is less than""

the other 'personifications' you are talking about appear to be suggestions and analogies. They are not true or false, merely useful or not useful. And I suspect that what that mathematician at princeton was doing was trying to explain to you some of the shorthand that mathematicians often use to explain the underlying gist of their work. For instance, I often say things like: using derived categories is the morally correct way to define cohomology.
I am drawing an analogy about the importance of the mathematics, but you would be foolish to draw the conclusion there is actually anything ethically correct in this choice.

23. Apr 13, 2005

### Moonrat

arildno, sorry I missed your post earlier,

Yes, I can see that..

I also see that and I certainly hope it doesn’t read that I am suggesting otherwise, however, we are still left with numbers none the less. And again, I am only identifying the relationships of these numbers to each other. It doesn’t matter, at least from this POV that I reference, how these numbers are used.

Hmm, that is an interesting thought indeed! The history of perception in relationship to number…Have you read the book ‘Zero, the History of a Dangerous Idea’? It goes into some of this…

But what I am suggesting is of course functioning in math at least as perception, there is a built in perception quality that is ternary in nature, and if this did not exist, there would be no 'math' by default..without these qualities that are found in 0, 1, and 2, we would not be able to 'distinguish' conceptual objects from external objects..

Lol, well, I can sure accept that, I certainly hope I am not giving the impression of assuming that this ‘should’ be applicable to mathematics, I am just asking how is this basic distinction referenced as 0, 1, and 2 can be understood in mathematical principles…which your saying that it cannot be understood it mathematical principles, but it does have a tertiary relationship in perception.. (is not ‘tertiary’ also a mathematical principle, or no?)

Hmmm, I am not sure if I follow, so if I don’t, PLEASE let’s elaborate on this a bit.

First off, from what I understand (very primitively in this regard, yes I admit) 0 and 1 is base two counting just like 0, 1, and 2 is base three counting. So binary systems create ‘simple choice’. Either this, or that.Distinguishing ONE thing from the other ONE thing. Now, this, or that, may both have value, however, one is always off and the other always on. Off is to 0 what on is to 1, no? 1 turns on it’s function, and 0 turns it off. Two distinct states.

If this sounds jumbled, then let me put it this way, we can apply binary counting to a ternary system, I can explain this philosophically, but certainly not mathematically, however, I do assume that since I can find a pattern, one must therefore be said to exist and thus must be able to be quantified into a mathematical expression.

Yes, I can see that. However, the relationship of 0 to 1 is always the same when we ‘divide, add, and multiply’, no?

MR

24. Apr 13, 2005

### arildno

All right:
To clarify the term "binary operation":
This does NOT refer to writing numbers in a binary base rather than a decimal base.

A binary operation means that you pick out two elements from a set and "produce" from them according to a given rule another element in the same set.

For example, addition is basically a binary operation in that you pick out two numbers (i.e, elements) and, by the rule of "adding" gain another number.

0 is a number called the additive identity (or neutral element), in that whenever 0 is one of the two elements you add, the other being, say, "a", your output is "a".
1 is analogously the multiplicative identity for the binary operation "multiplication".

That is what I meant with 0 and 1 being similar, in that they fulfill similar roles in distinct binary operations.

Last edited: Apr 13, 2005
25. Apr 13, 2005

### CRGreathouse

Philosophy, to be sure!

I can see a particular argument for 0, 1, and infinity as the building blocks for numbers (taken to be the set $$\{0,1,2,\ldots\}$$ adjoin infinity): 0 is the base element, and is the successor of no other; 1 is the 'typical' number, the first successor of 0, and the additive building block of the counting numbers (1, 1+1, 1+1+1, ...). Infinity is the only 'number' that is its own successor.

However, outside of some unusual philosophy, I can't see the relationship between 0 and mystery, 1 and true, or 2 and false. That's arbitrary at best. This is better done as abstract algebra, perhaps....

T, F, U (representing true, false, unknown). Would you like to define for us how you think these should combine? True and true is true, mystery and mystery is mystery, but what of the other 7 combinations? Maybe then we can better understand how these relate to numbers and give you input regarding how well 0, 1, and 2 work for these.

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