spooky3 Posted April 19, 2012 Share Posted April 19, 2012 Nope, because that implies that infinity has a size, which by it's very definition, it doesn't. Double infinity is equal to infinity. To state otherwise would imply that there were numbers larger than infinity, which there isn't. Look, even Lisa Simpson understands it! If "infinity" is interpreted as any specific transfinite cardinal number κ ≥ \aleph_0 in cardinal arithmetic, then "infinity plus 1" = κ+1 = κ. http://en.wikipedia.org/wiki/Infinity_plus_one EDIT: oops, wrong quote. Even though that last one states that afterwards it is infinity, but at the point of calculation it is theoretically larger. In mathematics, infinity plus one has meaning for the hyperreals, and also as the number ω+1 (omega plus one) in the ordinal numbers and surreal numbers. Link to comment Share on other sites More sharing options...
Mecky Posted April 19, 2012 Share Posted April 19, 2012 Right ot wrong, would it change anything? I certainly can't see it changing peoples' views. Link to comment Share on other sites More sharing options...
MrSmith Posted April 19, 2012 Share Posted April 19, 2012 Read the link, a subset and a superset of an infinite set can all be considered to have the same cardinality... Adding 1 to an infinite set doesn't make it larger. This is why an infinite universe can still expand without getting bigger. Link to comment Share on other sites More sharing options...
MrSmith Posted April 19, 2012 Share Posted April 19, 2012 You did say they were wrong about it though, implying that they don't understand it. Some scientist doesn’t think that an infinite universe is possible, whilst some scientists do think it’s possible, therefore some scientists are wrong about infinity. I should have said some instead of many, my bad sorry. Link to comment Share on other sites More sharing options...
HeadingNorth Posted April 19, 2012 Share Posted April 19, 2012 As you say, while we can prove that a set of all integers from 0..∞ has less items than a set of all real numbers from 0..∞ (or even a set of all real numbers between 0..1), but, both sets have ∞ items in them, and while of different lengths, both lengths are equal to ∞. "Equal to infinity" is a meaningless phrase. Both sets have an endless number of items in them, but they are not "both equal to endless" because endless is not a number. Link to comment Share on other sites More sharing options...
HeadingNorth Posted April 19, 2012 Share Posted April 19, 2012 Lets say we've got the two sets - one of all integers, and one of all real numbers. There's currently more real numbers in our set than integers, so we add another load of integers to our set (∞+1 is a valid (albeight undefined) number, so we can add all the integral one of them to our integer set), until we've got as many entries as our real numbers set. ∞+1 is not a valid number; ∞ isn't a valid number, it's a quality. You can perform arithmetical operations on it, but the answers you get won't obey the rules of arithmetic because you're not working with numbers. Link to comment Share on other sites More sharing options...
davi Posted April 19, 2012 Share Posted April 19, 2012 Who is 'nature'? Is that like Gaia theory or something? Not who is nature, that refers to "human". But what is nature, as that has been around longer than humans need to label and understand things. String theory can be explained better by Sheldon Cooper! Link to comment Share on other sites More sharing options...
spooky3 Posted April 19, 2012 Share Posted April 19, 2012 Not who is nature, that refers to "human". But what is nature, as that has been around longer than humans need to label and understand things. ... It's you who is referring to nature as having knowledge. Gaia Theory looks at the planet Earth as a system like you sort of described, you should read up. Mankind is continuously chasing after knowledge that nature already knows, ... Mankind is part of the natural world! Link to comment Share on other sites More sharing options...
Karis Posted April 20, 2012 Share Posted April 20, 2012 Yes, it's called life & study. 26+ years of my life not watching Coronation Street and accumulating knowledge and wisdom of ancient and modern man, years of supernatural experiences including UFO encounters with multiple witnesses, if you could read my mind and the acquired knowledge then please help yourself. So basically, you've spent 26 years studying fragments of knowledge and drawing your own wild assumptions? And of COURSE UFOs had to come into the story at some point... Link to comment Share on other sites More sharing options...
Cyclone Posted April 20, 2012 Share Posted April 20, 2012 Some scientist doesn’t think that an infinite universe is possible, whilst some scientists do think it’s possible, therefore some scientists are wrong about infinity. I should have said some instead of many, my bad sorry. This doesn't show a problem with the understanding of infinity, it shows a lack of knowledge (which we are aware of) in our understanding of the universe. There are several hypotheses about the nature of the universe, at the moment we don't have the evidence to test and disprove any of them, so we keep them all available as possible. It's science working perfectly, not a failure at all. Link to comment Share on other sites More sharing options...
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