# What is Infinity?

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i think if soemone posts a question in a mathematics forum about soemthing you should answer it mathematically and not spout guff about "primordial chaos theory" and other such things. and that means that you should explain the stone-cech compactifications, and infinite cardinals and ordinals. and when people ask for claridication then do so. if you want to explain something that isn't mathematics then say so and tell them where they should have posted the question if that was the material they were enquiring about. now, stop being part of the problem.

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Ok. I will try to give an example to make it simple.
And I shall try to make physical sense out of this, as you are clearly intending a physical, rather than mathematical explanation.

You are on the railway (no trains are coming),
Now, it is not clear whether this railway line runs on a plane or a large sphere, but I shall hold on this detail until it becomes necessary to proceed.

and the lines are perfectly parallel from your POV standing in their middle.
Now either the lines are parallel, or they are not. This has merely to do with the space in which the lines exist and the definition of parallelism in that space. It should have nothing to do with my POV. In fact, in my POV, the lines appear to converge, so I would hardly call them parallel.

You stare at the horizon where they vanish from your perspective.
Now physically, and ideally, everything up to the horizon is within sight, since it lies within my line of sight. On the plane, there is nothing beyond the horizon - from a non-zero height above the plane I can see every point on the plane and no point is obscured by another. On the sphere there is indeed a large surface area that exists beyond my horizon. And on the sphere, the railway line does indeed vanish from sight beyond the horizon. Since this is what you claim, it follows that you are talking about a situation on a sphere (or similarly closed 2D surface).

In fact, the rails continue beyond the point at which you significantly see, and into the zone of insignificance where you cannot see.
Unless you are now talking about practical limits to sight from dispersion and minimal detectable signals, there is no difference between 'seeing' and 'significantly seeing'. But in this case can only talk about finite distances, so this can not be. Hence, 'seeing' is synonymous with 'significantly seeing'.

The lines converge into a single point at infinity from your perspective,
A contradiction. On the sphere, the lines do not converge to a point. On the plane they do, but this possibility was previosly ruled out. So we are at an impasse and can not proceed.

Please eliminate this contradiction by changing one or both of the offending statements.

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why don't you tell us why do we have to truncate the infinite decimal figures of pi?
Just a guess here, but might it be because we only have a finite time to write down the decimal representation ?
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you should answer it mathematically and not spout guff about "primordial chaos theory" and other such things.

You are being notified to be posting a spiteful comment with a quoting that was not posted on this thread by me. However, Phi for All is a biased full of shaving cream God and increased my warning level to 10 points as a sacrificial goat whose blood is for your salvation. Of course it would be much easier for all of you to unsubscribe me if that option existed rather than torturing each other.

What really worries me about all of you as human beings connected on the Internet, is that the average conduct is obviously much lower than anything that could be evaluated as good conduct, and any philosophical value of power is exercised tyrannically.

I was thinking the other night about how much I would loose if I unsubscribed or was permanently banned from here.

Emm. <thinking again>

Absolutely nothing.

On the other hand, you loose a payable X-professor who has strong ideas for sharing. So if you seek good debates let us do it, less your childish whining and laughable punishments. Then there is always that overvalued dignity and feelings of pseudo-dominance and power, where it would be best for you to permanently ban me right away.

I promise I shall not hold any hard feelings, so do what you wish to do, but I shall not hold back my feelings and my intellectual judgement and that I have to tell you that I was on topic and you went off topic and that you are all full of shaving cream.

Now give us a proof demonstrating that "Significance" as a topic is irrelevant to "Infinity" as a topic, if you dare, and you are being openly challenged, I mean both of you.

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Read post 27 that you wrote that includes the phrase primordial chaos theory, which is teh only thing I recall quoting from you.

"X-professor"? I presume you mean ex-professor, or exprofessor. Of what? If it's mathematics I will eat my hat. (Professor in England would mean someone of international award winning research history, professor in the US might mean anyone attached to a univeristy with tenure. Is either of those applicable or do you mean associate or assistant professor? And again, of mathematics?)

As for the challenge, please feel free to post one mathematical link to an article containing the theory of "significance" to as related to infinity in any form that you may use to back up you assertions so that we may respond to said challenge with full information.

I only as that if you post authoritaively on this particular subforum you stick to dsicussing mathematics. And that request is only from me in the capacity of being a mathematician and nothing to do with any administration of this forum of which I have no part.

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You are being notified to be posting a spiteful comment with a quoting that was not posted on this thread by me. However' date=' Phi for All is a biased full of shaving cream God and increased my warning level to 10 points as a sacrificial goat whose blood is for your salvation. Of course it would be much easier for all of you to unsubscribe me if that option existed rather than torturing each other.

What really worries me about all of you as human beings connected on the Internet, is that the average conduct is obviously much lower than anything that could be evaluated as good conduct, and any philosophical value of power is exercised tyrannically.

I was thinking the other night about how much I would loose if I unsubscribed or was permanently banned from here.

Emm. <thinking again>

Absolutely nothing.

On the other hand, you loose a payable X-professor who has strong ideas for sharing. So if you seek good debates let us do it, less your childish whining and laughable punishments. Then there is always that overvalued dignity and feelings of pseudo-dominance and power, where it would be best for you to permanently ban me right away.

I promise I shall not hold any hard feelings, so do what you wish to do, but I shall not hold back my feelings and my intellectual judgement and that I have to tell you that I was on topic and you went off topic and that you are all full of shaving cream.

Now give us a proof demonstrating that "Significance" as a topic is irrelevant to "Infinity" as a topic, if you dare, and you are being openly challenged, I mean both of you. [/quote']

Man, what are you pissed for? They aren't cussing you out, they're trying to put up a problem that you must overcome so that if you do, you can prove your point. Your point is something about infinity, and these guys, DQW and Phi for All, are putting up an argument, and if you can re-explain your point so that it is good enough to easily understand, you can start over, and debate whatever you are trying to prove. There is no reason to just cuss out the forum and try to get banned from it.

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matt grime said "EL helped? but mathematically his post was garbage", and that was an unprofessional and emotional response with irresponsible and non-objective behaviour. He did not comment professionally on the way I extended the Weierstrass-Bolzano Theorem, and I dare him to say that this is off topic or that it is not mathematical as a subject. What did he say about the Zero Point as I defined it?

The subject from a mathematical point of view is intricately interrelated. Boundaries and limits are at the heart of the issue as shown by very well known mathematicians (not me). Divergence and convergence of numbers in sequences of infinite series are absolutely related too. Significance comes in with the mathematics of infinitesimals.

In science we can mean several things by "1", unity and one; it could be the name of a limit or the expanse of an interval, or a vector with a significant sign, etcetera.

The old paradox of Zeno was shown to be a trivial problem that was solved by calculus.

It is almost impossible to separate mathematics from physics unless we are talking about very specific numerical relations.

If matt grime still thinks that the theory of chaos and the theory of fractals are not mathematical theories then I have to beg him to reconsider what he thinks before it turns out ugly.

One does not call what others post as garbage unless one is absolutely sure that it is, but if you simply do not understand it, one should refrain from such ad hominem remarks.

I was never off topic, and he who is in suspicion can demand from me to present the verbose version that exposes the unquestionable relation.

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As for the challenge, please feel free to post one mathematical link to an article containing the theory of "significance" to as related to infinity in any form that you may use to back up you assertions so that we may respond to said challenge with full information.

From Wikipedia:

And

{The concept of significant figures originated from measuring a value and then estimating one degree below the limit of the reading; for example, if an object, measured with a ruler marked in millimeters, is known to be between six and seven millimeters and can be seen to be approximately 2/3 of the way between them, an acceptable measurement for it could be 6.6 mm or 6.7 mm, but not 6.666666 recurring mm. This rule is based upon the principle of not implying more precision than can be justified when measurements are taken in this manner.}

That paragraph was from Wikipedia's second link.

"not 6.666666 recurring mm"

Can you see where significance of figures relates to a non ending decimal fraction (recurrence)?

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This may just be me, but I dont see how either of those links is significant !

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One thing to consider is that there is three contexts of infinity that you must take into consideration if you were wanting to fully understand the word and meaning in multiple contexts.Infinity can be found in nuber system where it can be treated as a number(in this context infinity does not exist), topological science such as certain seqences of numbers to converge to(in this context infinity does exist),measuring sizes of sets where it is a measurmentof the size of an infinite set(in this context,such "infinity" concepts do exist but there are more than one of them, since not all infinite sets have the same size. So there does not exist any one single "infinity" concept; instead, there exists a whole collection of things called "infinite cardinal numbers". Anyways, infinity is in my opinion an individuals stand point. A great link in my opinion is http://www.math.toronto.edu/mathnet/answers/infinity.html
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This may just be me, but I dont see how either of those links is significant[/i'] !

The first link relates significance to statistics, which is a mathematical branch, which means that the subject is not off topic.

The second link is extremely significant because it is about relating significant figures and infinite recurrence.

If you still do not see how those links are significant to significance and infinity I cannot help you. I am a biochemist, not a pharmacist.

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I think you'll find I said that some of your post was garbagr. post a link to "primordial chaos theory" (or stop changing you mind about what yopu are complaining about, i take it you are now not accusing me of misquoting you).

those links certainly contain the word signficant, but none of them are related to the first instance of your use of the word (railway lines meeting at points beyond the horizon at a point of insignificance). you cannot just randomly apply words as you deem fit.

I think some of the things you have mentioned are good. But I also think that a lot of it is garbage and a series of non sequiturs. That is only my opinion and only of *some* parts of what you have chosen to write in a way that implies you are knowledgable about these things, things that are nothing to do with any part of known mathematics.

I am perfectly happy to discuss chaos theory (or non linear dynamics, or dynamical systems) as necessary to any debate about infinity, if there is any. that still doesn't remove the fact that you talked about "primordial chaos theory" and its links to chaos theory (a branch of mathematics of less importance than many think).

As you say, you are a biochemist by training and presumably that is what you are an "X-professor" of. You may want to pay attention to what a mathematician has to say about your opinions of mathematics.

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I think you'll find I said that some of your post was garbagr.

Some rather than all makes you proportionally a bit rude rather than totally rude.

Would you like to argue the mathematics behind what I just said here?

post a link to "primordial chaos theory" (or stop changing you mind about what yopu are complaining about, i take it you are now not accusing me of misquoting you).

I thought that you already searched and found out "My theory" and that you were explicitly insulting me about it without discussing it. You did not comment professionally yet on the extension of W&B theory.

those links certainly contain the word signficant, but none of them are related to the first instance of your use of the word (railway lines meeting at points beyond the horizon at a point of insignificance). you cannot just randomly apply words as you deem fit.

Now, now, we are not supposed to be playing hide and seek or are we!

I can say whatever I wish to say as an opinion, not like you flaming me with ad hominem remarks.

You dared me to post "Any Link" that relates significance to infinity and I did.

Stop this straw man fallacy at once, please.

I dared you to prove that significance was absolutely unrelated to any concept of infinity and you failed; then you escaped by asking me to present the proof that they are related, which is what I did; and now you are slipping away by pretending that there was supposed to be first and second instances of words being written! What a farce! Perhaps it was much easier for you to realise that I was right and simply apologise and your apology was going to be accepted (then).

I think some of the things you have mentioned are good. But I also think that a lot of it is garbage and a series of non sequiturs.

Parsing your English defies sanity. Are you saying that a lot of what I mentioned is garbage out of which some is good! Or are you saying that a minimal of what I posted was good while the remaining majority was identified as garbage since you are an expert on identifying garbage on sight?

Please educate me about the criteria of garbage words, because I was under the impressions that only this {&*^%\$##@^&*(((^%%^&} is identifiable as garbage characters that no intelligent being can decipher.

If that was what you read in my post then change your browser.

I am perfectly happy to discuss chaos theory (or non linear dynamics, or dynamical systems) as necessary to any debate about infinity, if there is any. that still doesn't remove the fact that you talked about "primordial chaos theory" and its links to chaos theory (a branch of mathematics of less importance than many think).

If it was not important and not interesting for you, then do not bother yourself with such trivial knowledge.

As you say, you are a biochemist by training and presumably that is what you are an "X-professor" of. You may want to pay attention to what a mathematician has to say about your opinions of mathematics.

I was paying attention when nothing was said.

I am still paying attention and still nothing is being said.

I will still pay more attention but I will not hold my breath for something valuable to be said.

I extended on W-B theory by constructing a topological Zero Point as a boundary to define the absolute infinity, which is absolutely relevant to this thread, and you said utterly nothing professional as a comment, and rather you went spewing rude ad hominem remarks calling my post or some of it garbage.

Is that what you call a civilized response?

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Boundaries and limits are at the heart of the issue as shown by very well known mathematicians (not me). Divergence and convergence of numbers in sequences of infinite series are absolutely related too. Significance comes in with the mathematics of infinitesimals.
I may agree with the first two sentences. I still do not see the usefulness of "significance" - which I know only in the context of statistical deviations - in explaining infinite sets or points at infinity. And please do not forget that it was in neither of these contexts that you used the word. Your 'significance' had to do with line of sight or dispresion (at least in one specific example).

In science we can mean several things by "1", unity and one; it could be the name of a limit or the expanse of an interval, or a vector with a significant sign, etcetera.
While 'green' can be the color of an apple or the color of a leaf, it is still the same thing.

The old paradox of Zeno was shown to be a trivial problem that was solved by calculus.
What is the point of this statement ? You are merelysaying that an infinite series can converge. Okay, what's new ? You've already spoken for the usefulness of infinite sequences and ideas like convergence.

It is almost impossible to separate mathematics from physics unless we are talking about very specific numerical relations. Au contraire, mathematics exists ABSOLUTELY independently of physics, and I can't see that this independence is dependent upon "very specific numerical relations".

If matt grime still thinks that the theory of chaos and the theory of fractals are not mathematical theories then I have to beg him to reconsider what he thinks before it turns out ugly.
I shouldn't be speaking for matt, but I don't recall him saying any such thing. Please quote where he says this. And how does their being mathematical theories have anything to do with answering the OP's question ?

I was never off topic, and he who is in suspicion can demand from me to present the verbose version that exposes the unquestionable relation.
If a post requires added verbosity to reveal a relevance to the topic of discussion, then it is (at least in the absense of this verbosity) off topic.

If someone asks me for the equation of a straight line in cartesian co-ordinates, and in response, I talk about Minkowski, light cones, railway tracks, regression analysis, non-Euclidean geometries, Lyapunov exponents, waveguides and the least action principle, without ever writing down the needed equation, what have I achieved (besides telling someone that I know about all these things) ?

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Thanks for teaching me how to read. I'll keep that trick in mind.

The first link relates significance to statistics, which is a mathematical branch, which means that the subject is not off topic.
The length of my big toe is related to mathematics, but talking about my big toe does nothing to answer a question about defining "infinity".

The second link is extremely significant because it is about relating significant figures and infinite recurrence.
As relevant as the fact that I can not in general, represent the lengths of my toes (in some standard length unit) using a finite decimal representation.

If you still do not see how those links are significant to significance and infinity I cannot help you. I am a biochemist, not a pharmacist.
And apparently, not a mathematician either (unlike some other members here). I'll keep that in mind, the next time I ask for help.
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I am still at a loss of whether or not a ray is qualified as infinity. It starts from a point. Infinity doesn't start or end. A line doesn't start or end.

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Still waiting to hear what "primiordial chaos theory" is. It seems that your issue is that you write in an odd way (using your own terminology and addendums) about ordinary mathematics.

Incidentally, it isn't ad hominem to criticize the content of your post, criticism you are free to refute, though you haven't. It would be ad hominem if i insulted you about you personallyy (eg calling you an idiot. i don't think you are that). i do think that you are confusing and mixing up terminolgy, as one can easily see by looking at your response to being asked what you meant by "significance". Your response here was to say "ah, you criticized my use of signficance with respect to infinity, go on, show me that signficance has nothing to do with infinity" and then to post a completely unrelated link (a non sequitur, is my english that difficult to parse? how is it impossible to simultaneously think that you have some good topics but that your not posting well on them?). We wanted to know what *your* particular use of the word was in reference to railway lines meeting at infinity. THat was all. Your response was a non sequitur.

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I am still at a loss of whether or not a ray is qualified as infinity. It starts from a point. Infinity doesn't start or end. A line doesn't start or end.
If the set of positive real numbers is a "ray", then it is an infinite set.

The set of all (non-negative and negative) real numbers is a "line", and that too is an infinite set, and is of the same "size" as the first set.

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I am still at a loss of whether or not a ray is qualified as infinity. It starts from a point. Infinity doesn't start or end. A line doesn't start or end.

what do you meant by "qualified" as infinity?

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I understand it because the universe supposedly has infinite expansion.

Plus since we are analog beings we can work to an infinite amount of possibilities.

Infinity is a great thing.

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I understand it because the universe supposedly has infinite expansion[/u'].
That is incorrect.
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You don't think the universe is unlimited?

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It's not unlimited.

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I'd like to think differently. But this topic is about infinity.

So if the universe has a limit than so does the number system. Thus taking away the idea that inifinity actually exists.

Imagine you have a bunch of foam numbers all collected together to resemble a number in the number system. The universe would eventually get full and couldn't hold anymore. Hmm..

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"So if the universe has a limit than so does the number system."

what has the physical property of finiteness or otherwise of the universe got to do with the fact that the natural numbers are not a finite set?

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