DannyTR Posted September 21, 2018 Posted September 21, 2018 https://en.wikipedia.org/wiki/Measure_problem_(cosmology) Two beaded cows as likely as one headed cows? A paradox surely. Paradoxes are indicative of an underlying logic error. In the case of the measure problem, it is probability that fails us. Why? Because we are plugging in the Actually Infinite as a real number. The Actually Infinite is an illogical concept that does not exist mathematically or in the material world. Infinity is defined in maths in two major ways: - Calculus. The limit concept. Tending to but never reaching Actual Infinity - Set theory. Actual completed infinite sets are allowed, IE Actual Infinity. How is Actual Infinity defines in set theory? It’s just an axiom that says something equivalent to ‘actual infinite sets exists’. So Actual Infinity is undefined in mathematics. Further more, it’s easy to prove that Actual Infinity is not a number: - There is no number X such that X > all other numbers - Because X+1 > X - Therefore Actual Infinity is not a number. So so a simple solution to the measure problem seems to be dropping the infinite universe...
studiot Posted September 21, 2018 Posted September 21, 2018 On 9/21/2018 at 12:53 PM, DannyTR said: https://en.wikipedia.org/wiki/Measure_problem_(cosmology) Two beaded cows as likely as one headed cows? A paradox surely. Paradoxes are indicative of an underlying logic error. In the case of the measure problem, it is probability that fails us. Why? Because we are plugging in the Actually Infinite as a real number. The Actually Infinite is an illogical concept that does not exist mathematically or in the material world. Infinity is defined in maths in two major ways: - Calculus. The limit concept. Tending to but never reaching Actual Infinity - Set theory. Actual completed infinite sets are allowed, IE Actual Infinity. How is Actual Infinity defines in set theory? It’s just an axiom that says something equivalent to ‘actual infinite sets exists’. So Actual Infinity is undefined in mathematics. Further more, it’s easy to prove that Actual Infinity is not a number: - There is no number X such that X > all other numbers - Because X+1 > X - Therefore Actual Infinity is not a number. So so a simple solution to the measure problem seems to be dropping the infinite universe... Expand Does this ramble have a point for discussion. If so what are we supposed to be discussing? Further why is this posted in Astronomy and Cosmology when it seems basically a mathematical proposition?
DannyTR Posted September 21, 2018 Author Posted September 21, 2018 I’d argue that if actual infinity can’t exist mathematically or in the material world, it cannot exist in cosmology, IE time and space and the universe are finite.
Strange Posted September 21, 2018 Posted September 21, 2018 On 9/21/2018 at 1:26 PM, DannyTR said: I’d argue that if actual infinity can’t exist mathematically or in the material world, it cannot exist in cosmology, IE time and space and the universe are finite. Expand Infinity does exist mathematically; it is well defined. As for whether it exists in the real world, that depends whether the universe is infinite or not! On 9/21/2018 at 12:53 PM, DannyTR said: Therefore Actual Infinity is not a number. Expand Yep. We know that. 1
DannyTR Posted September 21, 2018 Author Posted September 21, 2018 On 9/21/2018 at 2:04 PM, Strange said: Infinity does exist mathematically; it is well defined. As for whether it exists in the real world, that depends whether the universe is infinite or not! Expand It is only defined using an axiom saying it exists, they don’t prove it exists. https://en.m.wikipedia.org/wiki/Axiom_of_infinity That axiom is Wrong. It’s easy to prove there is no largest number and actual infinity does not exist in the material world... so the axiom is wrong.
Strange Posted September 21, 2018 Posted September 21, 2018 On 9/21/2018 at 2:12 PM, DannyTR said: It is only defined using an axiom saying it exists, they don’t prove it exists. https://en.m.wikipedia.org/wiki/Axiom_of_infinity That axiom is Wrong. It’s easy to prove there is no largest number and actual infinity does not exist in the material world... so the axiom is wrong. Expand The axiom is saying an infinite set exists, not defining infinity. As that page says, it can also be phrased in terms of a set contains all the integers (which we can prove are infinite, as you say). Quote It’s easy to prove there is no largest number Expand Saying “there is no largest number” is pretty much the definition of infinity. Quote actual infinity does not exist in the material world Expand And you can’t say that because the universe might be infinite
DannyTR Posted September 21, 2018 Author Posted September 21, 2018 The universe is part of the material world so I’d argue the universe cannot be Actually Infinite. Give me an example of the actually infinite from nature. There are none. IE: This is empirical evidence that the Actually Infinite does not exist.
studiot Posted September 21, 2018 Posted September 21, 2018 I still say this is in the wrong place as all the discussion has been mathematical. Infinity of any flavour is not defined in cosmology. Further your contention is really a speculation. On 9/21/2018 at 1:26 PM, DannyTR said: I’d argue that if actual infinity can’t exist mathematically or in the material world, it cannot exist in cosmology, IE time and space and the universe are finite. Expand Mathematically, of course various infinities exist and are numbers. it just depends which number system you mean. You might just as easily and just a swrongly contend that 0.553 is not a number because there is no such number in the integer number system or that Pi is not a number because there is no such number in the rational number system or that (5.+3i) is not a number because there is no such number in the real number system. Infinity exists in the extended number for instance. https://en.wikipedia.org/wiki/Extended_real_number_line Alternatively you can look at projective geometry as perhaps more relevant to cosmology that has a single infinity. https://en.wikipedia.org/wiki/Projective_geometry
Sensei Posted September 21, 2018 Posted September 21, 2018 "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."... Albert Einstein
studiot Posted September 21, 2018 Posted September 21, 2018 (edited) On 9/21/2018 at 2:43 PM, Sensei said: "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."... Albert Einstein Expand But dear Albert was being facetious. The size of any set of all real numbers that lie between any pair of real numbers is infinite. Edited September 21, 2018 by studiot 1
DannyTR Posted September 21, 2018 Author Posted September 21, 2018 (edited) Need to be clear about language at this point: https://en.wikipedia.org/wiki/Actual_infinity - The points on a number line is only a potential infinity not an actual infinity. - As you look finer, you see more points so it tends to infinity but never actually reaches actual infinity. As in a limit. Never reaches infinity. - Physically, it’s impossible for matter to exist with size 1/oo, so you would run out of resolution before you reached actually infinite points - But an infinite set has already reached actual infinity which is impossible. You cannot construct an actually infinite set so by extension you cannot have an actually infinite number of points on a line segment. Edited September 21, 2018 by DannyTR Clarity
Strange Posted September 21, 2018 Posted September 21, 2018 On 9/21/2018 at 2:28 PM, DannyTR said: Give me an example of the actually infinite from nature. Expand The universe (if it is infinite). Your argument that the universe is not infinite seems to be based on the premise that physical things cannot be infinite. This is the fallacy of begging the question. On 9/21/2018 at 3:09 PM, DannyTR said: - But an infinite set has already reached actual infinity Expand No it hasn't. That would mean that infinity was a number, and we all agree that it isn't. On 9/21/2018 at 3:09 PM, DannyTR said: Physically, it’s impossible for matter to exist with size 1/oo Expand 1/oo is undefined, so the statement is meaningless.
studiot Posted September 21, 2018 Posted September 21, 2018 (edited) On 9/21/2018 at 3:09 PM, DannyTR said: Need to be clear about language at this point: https://en.wikipedia.org/wiki/Actual_infinity - The points on a number line is only a potential infinity not an actual infinity. - As you look finer, you see more points so it tends to infinity but never actually reaches actual infinity. As in a limit. Never reaches infinity. - Physically, it’s impossible for matter to exist with size 1/oo, so you would run out of resolution before you reached actually infinite points - But an infinite set has already reached actual infinity which is impossible. You cannot construct an actually infinite set so by extension you cannot have an actually infinite number of points on a line segment. Expand Actual and potential infinities are an outmoded concept of the Ancient Greeks, who did not have the benefit of another two and a half thousand years of development. All the point in all my sets exist whether we have listed them or not, as do the sets themselves. But in any case I am talking about the measure of the sets, not the points or any limiting process. There is no need for any process or 'reaching of infinity', whatever reaching of infinity means. Kindly address my points in modern terms. Edited September 21, 2018 by studiot 1
taeto Posted September 21, 2018 Posted September 21, 2018 On 9/21/2018 at 3:09 PM, DannyTR said: https://en.wikipedia.org/wiki/Actual_infinity Expand It is a wikipedia page maintained by crackpots, its purpose is to vandalize wikipedia. It has nothing at all to do with mathematics. 1
mathematic Posted September 21, 2018 Posted September 21, 2018 (edited) The expression \int_0^\infty f(x)dx works for mathematicians. Edited September 21, 2018 by mathematic typo for latex
MigL Posted September 22, 2018 Posted September 22, 2018 You are arguing against the universe being infinite by saying no ( physical ) finite subsets of it are ??? I don't think that's valid logic. 2
Strange Posted September 22, 2018 Posted September 22, 2018 On 9/22/2018 at 12:14 PM, MigL said: You are arguing against the universe being infinite by saying no ( physical ) finite subsets of it are ??? I don't think that's valid logic. Expand By that "logic", the natural numbers can't be infinite because I can count from 1 to 10. (I can count further than that, by the way.)
studiot Posted September 22, 2018 Posted September 22, 2018 On 9/22/2018 at 12:14 PM, MigL said: You are arguing against the universe being infinite by saying no ( physical ) finite subsets of it are ??? I don't think that's valid logic. Expand A good summary +1
DannyTR Posted September 22, 2018 Author Posted September 22, 2018 On 9/22/2018 at 12:16 PM, Strange said: By that "logic", the natural numbers can't be infinite because I can count from 1 to 10. (I can count further than that, by the way.) Expand The natural numbers are potentially infinite, they cannot be Actually Infinite mathematically: there is no number X>all N because X+1>X. Actual infinity cannot exist in the material world either. What is such an illogical concept doing in the core of set theory?
Strange Posted September 22, 2018 Posted September 22, 2018 On 9/22/2018 at 12:35 PM, DannyTR said: The natural numbers are potentially infinite, they cannot be Actually Infinite mathematically Expand What does that mean? It is gibberish. Quote : there is no number X>all N because X+1>X. Expand Yes. That is the definition of them being infinite. On 9/22/2018 at 12:35 PM, DannyTR said: Actual infinity cannot exist in the material world either. Expand You keep repeating this claim. Where is the evidence?
studiot Posted September 22, 2018 Posted September 22, 2018 I will try one more time to get a response, before reporting the OP for lack of engagement with questions. Danny please tell me your exact definition of finite?
Strange Posted September 22, 2018 Posted September 22, 2018 On 9/21/2018 at 12:53 PM, DannyTR said: So so a simple solution to the measure problem seems to be dropping the infinite universe... Expand As we don't know if the universe is finite or infinite, this would be premature.
DannyTR Posted September 22, 2018 Author Posted September 22, 2018 On 9/22/2018 at 12:57 PM, studiot said: I will try one more time to get a response, before reporting the OP for lack of engagement with questions. Danny please tell me your exact definition of finite? Expand - finite is within bound, IE fully defined - Infinite is without bound, IE not fully defined IE undefined.
studiot Posted September 22, 2018 Posted September 22, 2018 On 9/22/2018 at 1:44 PM, DannyTR said: - finite is within bound, IE fully defined - Infinite is without bound, IE not fully defined IE undefined. Expand Thank you. So by within bound do you mean has a boundary? If so, is that boundary part of whatever is finite or not part of it? What is beyond that boundary? If not what does within bound mean?
Strange Posted September 22, 2018 Posted September 22, 2018 On 9/22/2018 at 1:44 PM, DannyTR said: - Infinite is without bound Expand Like the integers, then.
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