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 Does infinity exist? •Space and Time in Language Resident Usergroup: Members Joined: May 19, 2010 Total Topics: 0 Total Posts: 108 #41 - Quote - Permalink Posted May 20, 2010 - 10:00 AM: longfun wrote:Why not turn it around and make it true. Instead of going inward you can draw around it, and find infinity again.This is still not possible. Infinity is only possible theoretically. Let us stipulate to any conditions that you want, such as outside the circle. It would become impossibly impractical before too long. Even more important, a person, including all descendants, does not have an infinity of time in which to draw an infinity of circles, since life, of a person and of the species to include all descendants, is finite. •Space and Time in Language Resident Usergroup: Members Joined: May 19, 2010 Total Topics: 0 Total Posts: 108 #42 - Quote - Permalink Posted May 20, 2010 - 10:31 AM: Bisc wrote:Here's an example of infinity in reality. Under the general theory of relativity time stops when an entity reach the speed of light. Therefore from the point of view of a light particle it would reach it's destination instanteously, no matter how far it is. To the light particle, it's speed is infinite.You raise an interesting point, and I will have to give it some thought. Still, I wonder...Is the speed in this case really infinite? Speed is defined as the distance per unit time, or the change in space divided by the change in time. Therefore, calculation of the speed involves division. If the change in time is zero, then the result of division is undefined, rather than infinite. Is this wrong? •Bisc Initiate Usergroup: Members Joined: Apr 13, 2010 Total Topics: 0 Total Posts: 51 #43 - Quote - Permalink Posted May 20, 2010 - 1:03 PM: Space and Time in Language wrote: You raise an interesting point, and I will have to give it some thought. Still, I wonder... Is the speed in this case really infinite? Speed is defined as the distance per unit time, or the change in space divided by the change in time. Therefore, calculation of the speed involves division. If the change in time is zero, then the result of division is undefined, rather than infinite. Is this wrong? We use mathematics as a tool to describe reality. If our mathematics fails to handle infinity doesn't mean that infinite doesn't exist in reality, it is just a failure of the tool. Another example is the density of a singularity is also infinite. •Space and Time in Language Resident Usergroup: Members Joined: May 19, 2010 Total Topics: 0 Total Posts: 108 #44 - Quote - Permalink Posted May 20, 2010 - 3:59 PM: Bisc wrote: We use mathematics as a tool to describe reality. If our mathematics fails to handle infinity doesn't mean that infinite doesn't exist in reality, it is just a failure of the tool. Another example is the density of a singularity is also infinite.I think that this is not a failure of the tool, but rather an example of the inappropriate application of the term infinite.I think that in both of your examples, you are attempting to apply what is essentially a mathematical definition of the term infinite to what is not mathematics, making it inappropriate. It is not a failure of the tool, but rather an example of where the theoretical does not apply in the practical.What you said is that light moves at the speed of light, and therefore that this speed is infinite from the perspective of the light. I am not so sure that there is utility in this statement by borrowing from mathematics what is not applicable outside of mathematics.Still, from the approach that you are using, I recognize that there are certainly mathematical infinities that have some degree of correlate in the real world. •longfun a layman next door Usergroup: Members Joined: Feb 04, 2009 Total Topics: 5 Total Posts: 1578 #45 - Quote - Permalink Posted May 20, 2010 - 11:32 PM: Space and Time in Language wrote:This is still not possible. Infinity is only possible theoretically. Let us stipulate to any conditions that you want, such as outside the circle. It would become impossibly impractical before too long. Even more important, a person, including all descendants, does not have an infinity of time in which to draw an infinity of circles, since life, of a person and of the species to include all descendants, is finite.Ok, you have a point. Try this one, if space is infinite, you don't have to draw anything, as the infinite amount of circles is also already there. Your only returning problem, as you pointed out already, will be to find infinite time to solve the infinite impracticality to count or even redraw them. Infinity is comparable to an empty set = {}Only the brackets are reversed infinity = }{ set or }={ •ssu PF Addon Usergroup: Sponsors Joined: Jun 02, 2007 Location: north Total Topics: 25 Total Posts: 2193 #46 - Quote - Permalink Posted May 23, 2010 - 3:10 PM: My opinion is that infinity presents us a problem in the logic of mathematics because our premises for mathematics have come from the need of measurement and counting. Natural and rational numbers have a very natural link to counting and measurement (and hence it is no wonder that math evolved in various cultures without any interaction between them: there is no historical father of mathematics that had an idea "Hey, lets have math!"). Other numbers or classes of numbers have emerged from finding "gaps" or mathematical problems that cannot be answered if we just assume the usual array of numbers. Zero as a number, pi or irrational numbers are most obvious examples in history. It is well noticing that introducing irrational numbers to math didn't make math at all illogical, even if it was a horrible find to the Greeks. What was illogical and false was only the assumption that "all numbers are rational", which people did believe in Ancient Times. Hence the basic problem is what we define to be math. Simply "the biggest" number is not acceptable: it obviously is something that cannot be measured.Yet infinity does pop up in so many places in math that it cannot be just avoided. If it then is, as it seems at least to me, an integral part of mathematics, the reasoning behind infinity has to be then totally logical and in harmony with everything else in math. Adding it as an axiom doesn't clear the philosophical problems. It's problem is in my view is seen in Cantors system of cascading system of bigger and bigger infinities. The obvious question for a layman hearing Cantors idea for the first time is what all these bigger and bigger infinities then add up if taken together. Well, by "adding them all up" we get into a paradox, and this is avoided by talking about "sets" and "classes" and forbidding "Set of all sets". Something similar to the way Russell "solved" his antinomy by type-theory. Simple questions ending up with a paradox, or an antinomy, do not make infinity (or math) illogical. I believe that a paradox simply states that we do not understand everything there is to understand from mathematics: a paradox is not something to be solved but an answer to be understood. The problem is likely to be the same type as the Greeks had with the irrationals. Their problem was a too narrow definition of what numbers are, which made their premise (all numbers are rational) false. Trying to "solve" the problem of irrationals...to make them somehow rational, simply doesn't work as one cannot square the circle (if pi would be a rational number, sure!). Many of people in Anciet Times likely didn't even notice that they made this kind of assumption as the idea of numbers not being divisible didn't cross their minds at all. Perhaps we have similar problems with infinity: we make assumptions about mathematics and numbers that we don't understand to be just our assumptions. And yes, I do believe that infinity exists...if numbers and mathematical objects can be said to exist. •Space and Time in Language Resident Usergroup: Members Joined: May 19, 2010 Total Topics: 0 Total Posts: 108 #47 - Quote - Permalink Posted May 24, 2010 - 12:58 AM: longfun wrote:Try this one, if space is infinite,This is quite a big if, which I doubt. you don't have to draw anything, as the infinite amount of circles is also already there.Circles in English or circles in geometry? Geometric circles cannot exist in the real world, so that is out. Circles in English, those that do have have enough dimensions to exist, are not already there, as they need to be drawn. Or, do you mean circle-like shapes that occur naturally in nature. If so, then perhaps you are correct, but since you use the word redraw then it seems like this is not what you mean.Your only returning problem, as you pointed out already, will be to find infinite time to solve the infinite impracticality to count or even redraw them. If only we had an infinite amount of time to ponder the difficulty of this problem. •Space and Time in Language Resident Usergroup: Members Joined: May 19, 2010 Total Topics: 0 Total Posts: 108 #48 - Quote - Permalink Posted May 24, 2010 - 1:04 AM: ssu wrote:And yes, I do believe that infinity exists...if numbers and mathematical objects can be said to exist.I think that numbers had a natural source, counting of cycles of nature. However, infinities did not arise until abstractions from the source led to theoretical situations. The set of natural numbers is infinite in theory, but not infinite in practice. Mathematical numbers and mathematical objects do exist, but only in the mind, and not in the real world. For example, a mathematical circle cannot exist in the real world. •MoeBlee aka I. Kabruob Usergroup: Members Joined: May 19, 2005 Total Topics: 10 Total Posts: 352 #49 - Quote - Permalink Posted May 24, 2010 - 7:11 AM: longfun wrote:Infinity is comparable to an empty set = {}Only the brackets are reversed infinity = }{ set or }={That has no apparent mathematical meaning. You might consult a textbook on set theory in which the subject of infinity is addressed mathematically. •Bisc Initiate Usergroup: Members Joined: Apr 13, 2010 Total Topics: 0 Total Posts: 51 #50 - Quote - Permalink Posted May 24, 2010 - 11:13 PM: Space and Time in Language wrote: I think that this is not a failure of the tool, but rather an example of the inappropriate application of the term infinite. I think that in both of your examples, you are attempting to apply what is essentially a mathematical definition of the term infinite to what is not mathematics, making it inappropriate. It is not a failure of the tool, but rather an example of where the theoretical does not apply in the practical. What you said is that light moves at the speed of light, and therefore that this speed is infinite from the perspective of the light. I am not so sure that there is utility in this statement by borrowing from mathematics what is not applicable outside of mathematics. Still, from the approach that you are using, I recognize that there are certainly mathematical infinities that have some degree of correlate in the real world. I am not sure what you mean by inappropriate. Density of a singularity and the speed of light from the perspective of the light particle are both infinity and both verifiable scientifically. Just because we humans cannot imagine infinity is just our own limitation and doesn't mean it can't exist.

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