Waldo Posted May 5, 2015 Author Share Posted May 5, 2015 Is 0.999999999etc the same as 1? There was another numberphile video on YouTube (sorry, can't find link), covering that exact question. I think they concluded, yes, it is the same. Link to comment Share on other sites More sharing options...
flamingjimmy Posted May 5, 2015 Share Posted May 5, 2015 Most mathematicians will tell you that 0.9 recurring is the same as 1. Link to comment Share on other sites More sharing options...
Waldo Posted May 5, 2015 Author Share Posted May 5, 2015 Most mathematicians will tell you that 0.9 recurring is the same as 1. ...and apparently, 1+2+3+4+5+6 ... up to infinity = -1/12 ---------- Post added 06-05-2015 at 00:33 ---------- Numberphile again.. Link to comment Share on other sites More sharing options...
davyboy Posted May 6, 2015 Share Posted May 6, 2015 ...and apparently, 1+2+3+4+5+6 ... up to infinity = -1/12 ---------- Post added 06-05-2015 at 00:33 ---------- Numberphile again.. so what is: 1+2-3+4-5+6-7+8-9....... Link to comment Share on other sites More sharing options...
flamingjimmy Posted May 6, 2015 Share Posted May 6, 2015 ...and apparently, 1+2+3+4+5+6 ... up to infinity = -1/12 ---------- Post added 06-05-2015 at 00:33 ---------- Numberphile again.. Oh yeah that's one of my favourites, I memorised the proof and have delighted in showing some of my coursemates. Link to comment Share on other sites More sharing options...
woolyhead Posted May 6, 2015 Share Posted May 6, 2015 (edited) Which infinity are you asking about, Waldo? The cardinality of the set of real numbers is greater than that of the set of natural numbers, both of which are infinite, but they are are different infinities. There are others, too. At least, that's what Cantor found, using logic. The question now is would you say that logic is only in the mind? Plato drew his "three worlds" picture showing the physical world as part of the mathematical world which is a part of the mental world which in turn is part of the physical world, showing how all these three things are part of and smaller than each other. I think the answer to your original question depends on your viewpoint, eg the physical world is a part of the mathematical world when viewed from the mathematician's point of view because he knows not only about the physical world but also about stuff which isn't to do with the physical world. When viewed form the viewpoint of the physical world however, what the mathematician knows is in his brain which is only a part of the physical world. ---------- Post added 06-05-2015 at 19:27 ---------- I thought so too, that is, time is a property of this instance of the universe we are part of, just like matter, laws of physics, etc, are all properties of this one particular universe. But all this universe, at least that part of it we know about, is inside my head. So why isn't the universe a property of my thinking? ---------- Post added 06-05-2015 at 19:35 ---------- Cantor's proof that there are numbers that could not be predicted by any routine used the idea of drawing a diagonal across a table of numbers and noting the number sequence that his pencil crossed, thus creating a number that couldn't have been in the original table. But that table was not infinite in size so it didn't contain all the possible numbers. So what did he actually prove? Edited May 9, 2015 by woolyhead Link to comment Share on other sites More sharing options...
Waldo Posted May 6, 2015 Author Share Posted May 6, 2015 But all this universe, at least that part of it we know about, is inside my head. So why isn't the universe a property of my thinking? Sorry for the short reply; it's actually a very interesting question (but it's late, and I've just got back from the Siverstone 10k, which I ran, in pouring rain, and I've got a bit cold)... I would think, that the universe, and your thinking; are the same thing. It's only your mind conceptualising, to create the notion of separate entities (i.e. itself, and, 'the universe'). You are the universe (perhaps not in it's entirety, more like the way your little finger is part and parcel of you). That's how I tend to see things; no doubt a lot of people would disagree. Link to comment Share on other sites More sharing options...
woolyhead Posted May 7, 2015 Share Posted May 7, 2015 (edited) Look Waldo, if my little finger were chopped off I would know about it, whereas if my head and brain were chopped off my little finger would know nothing. So brain and finger are no way the same thing. But somehow I don't think you really meant what I took your post to mean. I think it goes a lot deeper than my facile reply. There is an interesting fact about the collapse of the wave function in physics. Fundamental particles are best described by wave functions, which are said to collapse when the human mind perceives them. Wave functions are part of the universe according to physicists but they are collapsed by the mind. So presumably they aren't part of the mind. So they are part of the universe and since they represent objects (electrons and so on), these objects are part of the universe. But my brain is made of things like electrons. So you and Waldo seem to be right on one hand but wrong on the other. Edited May 20, 2015 by woolyhead Link to comment Share on other sites More sharing options...
swarfendor437 Posted May 7, 2015 Share Posted May 7, 2015 Well people may have missed the brilliant programme on TV covering the re-discovered works of the greatest mathematician that ever lived - Archimedes. Christian Monks were reliant on parchment and as it was in short supply, some of Archimedes had been recycled into religious texts. Through X-ray technology they discovered that Archimedes had in fact worked out the formula for infinity! That is my total input - I can't go on, and on, and on ... Link to comment Share on other sites More sharing options...
woolyhead Posted May 9, 2015 Share Posted May 9, 2015 (edited) Well people may have missed the brilliant programme on TV covering the re-discovered works of the greatest mathematician that ever lived - Archimedes. Christian Monks were reliant on parchment and as it was in short supply, some of Archimedes had been recycled into religious texts. Through X-ray technology they discovered that Archimedes had in fact worked out the formula for infinity! That is my total input - I can't go on, and on, and on ... It's brilliant! So what is the formula for infinity? I don't understand what you mean. What formula? ---------- Post added 20-05-2015 at 19:22 ---------- Unless you believe in the idea that everything that exists can one day cease to exist, its hard not to believe that it will exist for ever, without end, infinity. What about continuing to cut each piece of string into thirds, will there ever come a point in which there is nothing to cut in half. Yes, when the scissors can't resolve the microscopicall small piece of string. Also, what makes you think that our bodies will exist forever? Edited May 20, 2015 by woolyhead Link to comment Share on other sites More sharing options...
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