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Does infinity exist?

Cadrache
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Posted 08/15/09 - 03:42 PM:	#21
lol... need to write up a few more. There is another aspect to infinity. The difference between physicality and concept. You can physically draw the circle and 'draw' infinite lines if it were possible to draw lines of 0 width. (which you can by way of one of Poincare's point particle systems) Unfortunately there is an actual 'end point' to the number of lines that can be drawn due to limitation of the Planck length. In other words, if the Planck length is .008mm, and you have a circle of 3 cm then the value for infinity would be 3750. (125x.008=1mm x 3 x 10) Differences in numbers might arise if you decide to run trig systems. (you end up with 3750 hypotenuses.) Yet the concept of infinity can go beyond the physical infinite number. You can have a conceptual circle of 3 cm which contains 20 trillion lines! This is due in part due to the membrane upon which a function lays upon. (See Reinemann's work.) This 'proof' unfortunately disproves the equality laws of mathematics. We cannot exchange this 3 over here for that 3 over there.
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

WastingTime
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Posted 08/16/09 - 02:09 AM:	#22
former wrote: I didn't say it's onto!. i said it's one-to-one. What you said, exactly was former wrote: f(a,b)=(a+b)^2+a+1 provide a one-to-one correspondance from N^2 to N A one-to-one correspondence is understood to be a bijection. One way or the other,it's doesn't change my original argument for there are alef_1 functions that are one-to-one and onto from N^2 to N You didn't prove that there are aleph_1 of anything. You have an incomplete argument which purports to show that N and N^2 are equinumerous.
Don't waste your time or time will waste you

former
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Posted 08/16/09 - 02:27 AM:	#23
A one-to-one correspondence is understood to be a bijection. But it's not. You didn't prove that there are aleph_1 of anything. You have an incomplete argument which purports to show that N and N^2 are equinumerous No, I didn't prove. I merely made a statement. Right, I have an incomplete argument which I assume the reader can complete. And I have said how to complete it in the next reply. My original argument was about reduction of dimensions, in which to show that N^2 and N have the same cardinal is but one step. I didn't prove it is one-to-one. I didn't prove the fixing function make it onto. I didn't prove the reals could be built from N. I didn't prove the reduction of dimension is one-to-one and onto from R. I just gave a general direction. I didn't walk the way with you. Edited by hyena in petticoat on 08/19/09 - 09:16 PM. Reason: Illiteracy.

WastingTime
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Posted 08/16/09 - 02:52 AM:	#24
former wrote: But it's not. A one-to-one correspondence is understood to be a bijection. It's standard in math literature. Check your books. former wrote: No, i didn't prove. i merely made a statement Right, i have an incomplete argument which i assume the reader can complete. And i have said how to complete it in the next reply. You didn't make any sensible statements that could be completed. In post #17 you asserted that you were demonstrating a one-to-one correspondence between N^2 and N. That claim was false. After I pointed out that it was false you claimed that a one-to-one correspondence is not the same thing as a bijection (which is false), check your math books. Then you went off on a strange tangent saying that former wrote: One way or the other,it's doesn't change my original argument for there are alef_1 functions that are one-to-one and onto from N^2 to N Which is an even crazier claim. former wrote: My original argument was about reduction of dimensions uh huh...
Don't waste your time or time will waste you

AKG
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Posted 08/16/09 - 03:34 AM:	#25
Are you saying you can prove there are exactly Aleph_1 bijections from N to N²? Do you realize this amounts to proving the Continuum Hypothesis? Do you realize it's provably impossible to derive CH from the axioms of ZFC?
"The only reason we die... is because we accept it as an inevitability." -- Stewie "To enslave nuance to dogma is folly." -- Lord Hillyer

former
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Posted 08/16/09 - 03:51 AM:	#26
No, you are right, I used alef_1 to mean: "the cardinality of the reals" = 2^alef_0 while it denote "the smallest cardinal greater than alef_0". alef_1=2^alef_0 is ch. What i mean to say is that the bijections fron N^2 to N are 2^alef_0 Thanks for fixing that. Edited by hyena in petticoat on 08/19/09 - 09:15 PM. Reason: Illiteracy.

Anecades
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Posted 09/02/09 - 03:29 PM: Subject: For what it's worth	#27
The key to understanding the mathematical concept of infinity is breaking out of the assumption that it is a static number like 5. Infinity is a concept that denies quantification. As soon as you try to pin it down it is, by definition, more than that. So the concept of infinity is simply the human conception of something that is 'greater' or 'more' or 'a bigger number' than whatever it is that is being imagined or thought of. Therefore it is not a number and you can't apply mathematical operations on it (or if you do you drain the meaning from the whole equation.) My personal idea of infinity is more of along the lines of Wittgenstein's comment that goes something like: "If we take eternity to mean not infinite temporal duration, but a sense of timelessness then eternal life belongs to those who live in the present." Infinity is an experience that we slide into as we go about our lives. It's a muse that hides in art. It's a dream of scientists and mathematicians. It's a teaching tool. An attempt to comprehend a limit that can never be reached. It's fun stuff, but, as with any such concept, it leads to seriously isolating behavior when it's not recognized as a wonder of the human mental prowess and taken as something that can be found in the universe. The maths and sciences exist well within infinity's retreating boundaries and become more and more tenuous whenever they take a wild grasp out to reach it. Take Cosmology as a perfect example of this. Love it. Anecades

iamgreatbob
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Posted 09/23/09 - 02:57 AM:	#28
I believe that infinity is nothing more than an illusion. While I do not deny that it has truth as a mathematical concept, I do not believe that it can exist in reality. First of all, the set of infinity contradicts so many mathematical concepts that if infinity were not already accepted and I proposed it today I would be laughed at. Also, scientists believe both that the universe had both a moment of creation and that it is expanding. Just cause you can't find the end of something doesn't mean it's infinite. Who says that the universe won't someday just end? In fact, the bible says that it will. As for what is beyond our universe (if such a thing exists) maybe there is infinity. But since it is beyond our universe, that means that it doesn't have to contend with our universes rules. So anything contradicting infinity might not apply there. However, in our universe I think it is unlikely that there is anything that is actually infinite (although some things may seem infinite, they do have a definite start and end). That might be different outside of our universe, or it might not. I'm not saying that anyone else is wrong, I'm just stating my beliefs.

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