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#73
Mar1911, 06:09 AM

P: 178

You can't define infinity precisely any more than you can God you can only allude to it, to even try is sophistry at best and outright delusion at worst. I wouldn't mind but mathemeticians have large enough egos as it is lets face it they think they are special because they are good at maths. Being able to conceive of the inconceivable places them in a position where they are gods though and I find that humerous. If you are going to use a term at least make it something that remotely approaches what you are trying to describe, cause no matter how close you get to it it is always infinitely far away. Such a concept being countable or even countable as Cantor describes it makes a mockery of the whole definition. "There are only two infinities: The Universe and human stupidity and I'm not sure about the first one." The conceit is colossal isn't it really. And just what you'd expect from a field with very, very, very oversized egos, in fact infinitely large egos apparently, since their minds can grasp infinity and conceptualise it, even visualise it. As an axiom it is only consistent with itself, which is fine, the terms though are not infinities there is a definition problem there. What they should say is if we take this as actually representing the infinity of all numbers then it is not possible to diagonalise it given the lifespan of the universe without skipping all the steps in between and hence not really either deductively or inductively defining it. What instead we have is a non constructive proof, based on terms we cannot define we are claiming we can. Now this is ok but why use the term infinity for something it is not? Why use such a contentious term? I think I know why its again an ego issue. Perhaps not with Cantor, but with people who claim to have seen or grasped the infinite, they haven't but they will of course claim the impossible, because it flatters them to think they can achieve that which cannot be done, even by God and that is define something that is greater than the infinite or God. Cantor makes the distinction between actually infinite and aleph 0 quite clear, most mathematicians though would rather die than admit it isn't really infinite at all. 


#74
Mar1911, 06:26 AM

P: 2,179

[tex]\pi[/tex] is the ratio of the circumference of a circle to its diameter. You represent it everytime you draw a circle, no matter how crude.



#75
Mar1911, 06:31 AM

P: 178

You represent it is the key word but you cannot measure its accuracy to infinite places though can you. Or can you? Do you think you can? In fact you couldn't even measure if it approached pi to 1000 decimal places let alone a million or infinite decimal places. This is no more a pictorial representation of pi than the wave function is a pictorial representation of the photon. That cannot be known either. A circle is a representation of [itex] C=2\pi{r}[/itex] it can by definition though only be represented approximately, no matter how precise your tools are it is impossible to measure anything with infinite places to infinite places. It is not possible to draw a perfect circle. 


#76
Mar1911, 06:52 AM

P: 2,179




#78
Mar1911, 07:24 AM

P: 2,179

I think that there is some confusion here about the difference between math and physics. Physics is the science of measurement. Representation of ideas in mathematics is divorced from physical measurements.
On another point, it occurs to me that in the Reimann sphere, the north pole represents infinity quite nicely. 


#79
Mar1911, 09:02 AM

Sci Advisor
HW Helper
P: 2,280

So you're saying π isn't your favorite number?



#80
Mar1911, 10:12 AM

P: 178

This will do though: a. To stand for; symbolize: The bald eagle represents the United States. b. To indicate or communicate by signs or symbols: Letters of the alphabet represent sounds. 2. a. To depict in art; portray. b. To describe or present in words; set forth. 3. To present clearly to the mind. 4. To draw attention to by way of remonstrance or protest: Our parents represented to us the need for greater caution. 5. To describe or put forward (a person or thing) as an embodiment of a specified quality. 6. a. To serve as the official and authorized delegate or agent for. b. To act as a spokesperson for. 7. To serve as an example of: The museum had several paintings representing the artist's early style. 8. To be the equivalent of. 9. a. To stage (a play, for example); produce. b. To act the part or role of. What you have is a description of something that you cannot perceive portrayed in a manner you actually can or at least think you can but they are not epistemologically the same thing, one is based on a property, the other is an actual unbound unquantifiable entity; the maths infinite and the infinite everyone else uses and actually always has are not the same thing. Perception of the infinite regardless of how you want to dress it up is impossible in any definition maths or otherwise we can only allude to it or approach it asymptotically. You can either conceive of the infinite or you can't, you trust me can not. if you cannot conceive of it but only use the argument that property denotes existence then you are on pretty shaky ground in terms of definition, that would not even be a non constructive proof it would actually be a non sequitur; just because something has a property does not mean it exists, likewise it does not make it something that you can define either. God doesn't exist because he is the greatest thing you can imagine any more than aleph omega exists because it is the greatest cardinality. What's more you can't even comprehend the terms in the definition without infinite capacity in your mind any way which makes this all rather philosophically tenuous at best. Certainly doesn't make these axioms in any way provable without asserting they exist as x therefore they must exist, whether they are infinite or not is of course to a mathmetician beside the point. But I happen to think its important. What I said about the correct thread goes the same here too. 


#81
Mar1911, 10:14 AM

P: 178

You can't represent infinity in your mind any more than you can on paper, what you can do though is pretend you can. If you can encompass that which is beyond count and not just that that which is beyond even that in your mind though, great, you have done what no one else could ever do not even God. whether you call it the set of all numbers or spaszkar it still doesn't make aleph either conceptually the same as an infinity or physically the same. There are actual infinities conceptual or real and or physical and then there are those fake infinities that are allusions to infinity that maths bods use, they are not the same thing. Something Cantor himself pointed out at some length. Just how many angels can dance on the head of a pin anyway? Call it a Reimann sphere call it whatever you like it still isn't conceivable infinitely it is again another sort of allusion one that cannot be demonstrated given the finite nature of reality in any form except as a tenuous analogy at best. Ok I'm not answering any more questions in this thread so don't bother asking them, take it to the apt thread or don't. 


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