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Does zero contain everything?

Benkei
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Posted 06/25/09 - 04:19 AM:	#11
Let's assume: ∞ - ∞ = 0 Now, adding 1 and 1 on both sides of the equation gives me: 1 + ∞ - ∞ = 0 + 1 Since 1 + ∞ = ∞ and we assumed ∞ - ∞ = 0 , the derivation of the above second equation would be 0 = 1. This is untrue. Therefore, ∞ - ∞ is undefined.
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the.yangist
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Posted 06/25/09 - 10:00 PM:	#12
180 Proof wrote: Explain "all numbers". Explain "all possible". In what sense? Some syntaxes take universality to be primitive (∀, but I'll give you some of my own design to see if it makes a dent in whatever you think the objection you hold is, per your seeming insistence. We can take a step back and think of universality as a sufficient condition on which another primitive (perhaps of "quantity" (Quan.(t)) can be based), and we can take universality to be a proposal that, in the event that the term has a quantity greater than one, that some series of predicates can be made of those terms. Example: "All natural numbers are rational numbers." (Quan.(n) > 0) ⊃ (Nn ⊃ Qn) Since you're going to favor set-theoretic talk, you can think of this Quan.(t) operation in terms of the ordinality of any well-ordered subset of the set. A "possible world" can be defined as a conjunction of propositions that remain consistent and which are inconsistent with the conjunction of any negation to any sub-proposition within that conjunct. "All possible worlds" would then be the union of those complex propositions, so an infinite string of disjunctive conjuncts of propositions. 180 Proof wrote: Explain the material instantation (e.g. universe) of "an infinite set". "The set of all X" says nothing more than "the set of X". "Set of", or "class of", entails every instance (i.e. satisfaction of membership-rules) of the relevant concept so "set of all X ..." seems a distinction without a difference. Yeah, in contrast one could express "the set of some Z" but this qualification entails only "a subset of the set of Z". Wow! You mean that your objection to the use of the word all is in your insistence that it have a "material instantiation?" You're putting more constraints than I've ever heard anyone, mathematician or otherwise, do. Don't get me wrong. I think another redundancy theory is fine and good, but I don't see how your objection pans out without the assumption you've made above, that all of a natural language can only be meaningful with this "material instantiation" talk. You've basically excluded all abstraction, including numbers, from quantification in any natural language context. 180 Proof wrote: Translation: The set of natural numbers is a subset of the set of rational numbers. I see, and you can denote the set-to-subset relation in infinite numbers how without entailing something to the effect, "For all numbers, if that number is a natural number, then it is a rational number?" I think that you think my disagreement with you is about something that it is not. 180 Proof wrote: It works fine. IF n (0,1) = N, THEN n+1 = N. No problem. 'Mathematical induction', as I far as I can tell, is a membership-rule axiom (re: sets/classes). I really don't see, yang, what this has to do with my taking issue with Oysteroid's semantic faux pas & conceptual muddle. All I'm trying to point out is that formal expressions (e.g. [(n+1) - (n+1) = 0]) do not translate directly in to informal statements (e.g. "If the universe is actually made of math as some like Max Tegmark have suggested, and as is suggested in Wigner's paper on the unreasonable effectiveness of math, and as seems suggested by how well we can simulate physics with computers, then maybe ultimate reality is simply nothingness ...") without introducing conceptual confusions (see OP, paragraphs 1-3). That can all be done by pointing out all of the other conceptual muddles that have nothing to do with quantification.
"If it were not for the laughter, the Way would not be what it is." -- Laozi

Ich Werde
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Posted 06/28/09 - 01:17 AM:	#13
It contains nothing, but is the essence of infinity. It is not so much nothing, but a soul for the binary digits

Ich Werde
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Posted 06/28/09 - 01:18 AM:	#14
Ich Werde wrote: It contains nothing, but is the essence of infinity. It is not so much nothing, but a soul for the binary digits A foundation.

Minyun
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Posted 06/28/09 - 11:37 AM:	#15
I once asked something similar in a thread not so long ago, if nothing (zero) was the same as everything (infinity). It was met with heated debate, the one thing I learned from this, was that only you (when dealing with things you cannot prove) must decide what the truth is. Much of mass as we know it is of empty space... as well as full space. These two mix to form a reaction, an atom, for example (this is ofcourse if you subscribe to this belief). We will never reach a point in which we will know everything about a thing, thus there will always be empty spaces abound which need filling. These two 'elements' combine to form reality, they create 'nothing' and 'something'. This is a definition which divides and confuses. There is a common misconception that to be inquisitive and curious is a good thing, however it takes balance, sometimes we go further than we ought to and we land in a sea of complexities, wondering how it can all be so. The balance is justified by knowing when to be curious and when not to be curious. It takes a certain trust in reality to find that balance in a man. It might do you well to read the story of Icarus. What does it bring you, to know of the things beyond your immediate knowledge? Comfort? Pride? Trust? Everything? Ah, and so it turns again, and it comes back to everything. Then we wonder in confusion about it because we find it so hard to hold onto the bigger picture. We have become microscropes of the world, with our intention to know the bigger picture, this is folly as our goal will never be reached. So what is it that we ought to do in the case of learning wether zero contains everything? Must we simply abandon this thought outright? No. Accept that your truth is ultimate and understand that there are others like you. Else you may just end up arguing/searching for eternity - this is the bigger picture.

the.yangist
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Posted 07/01/09 - 04:49 AM:	#16
Zero is a number. Numbers do not contain everything. Therefore, zero does not contain everything. Q.E.D.
"If it were not for the laughter, the Way would not be what it is." -- Laozi

jsidelko
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Posted 07/21/09 - 02:46 PM:	#17
After I recently opened a thread, "Does everything equal nothing?", I discovered your earlier thread, "Does zero equal everything?" had been discussing the same topic.Both our positions appear to be similar. Incidentally, this idea has been called the zero ontology by the philosopher, Arthur Witherall and the writer, David Pierce.http://www.hedweb.com/witherall/zero.htm. We can discuss this topic because we happen to live on one of the positive or negative branches in a universe of which the totality of existence is zero.
thanatos

UnicursalSeal
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Posted 07/29/09 - 08:27 AM:	#18
If X=~X, then ~X. I say that that is most intuitive. If X exists, which means that any number belonging to any body of any kind exists, then there must logically be ~X, which follows that as longs there is X, there must always be ~X. Put it into perspective: X=Man, thus X=Life ~X= Death, therefore Life=Death One does not exist without the other, therefore no number can exist without its corrollary. No body exists without it antithesis. There is one exception: Zero Zero is the moot point between that which exists and that which does not. It is the probability of something that will exist or won't exist. In it is potential, or none at all.

mrousseau
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Posted 07/31/09 - 01:54 AM:	#19
Math is a tool we use to derive statements which follow from others according to set rules we have specified. The application of mathematics to reality comes with the burden of having to justify it's usefulness (and not truth!) in some particular instance.

longfun
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Posted 07/31/09 - 04:18 AM:	#20
Benkei wrote: Let's assume: ∞ - ∞ = 0 Now, adding 1 and 1 on both sides of the equation gives me: 1 + ∞ - ∞ = 0 + 1 Since 1 + ∞ = ∞ and we assumed ∞ - ∞ = 0 , the derivation of the above second equation would be 0 = 1. This is untrue. Therefore, ∞ - ∞ is undefined. I think you made a reasoning error.. -1 + ∞ - ∞ = 0 + 1 -1 + ∞ = 0 + 1 + ∞ Since -1 + ∞ = 1 + ∞ and we assumed ∞ - ∞ = 0 , the derivation of the above second equation would be 0 = 0. This is true. Therefore, ∞ - ∞ is defined. not? Also ∞ = 0 is logical ∞ = potentiality 0 = objectivity Only religious people would look to find something different
I'm Long and I'm playing the greatest game of all.

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