Thelema Posted July 8, 2013 So Peano naturally assumes that the sequence of integers goes something like dude dude plus one etc but can you actually PROVE that there is no integer between 0 and 1? >>> I Don't think so! 1 Share this post Link to post Share on other sites

Yeti101 Posted July 8, 2013 Your posts are awesome lately Thelema. 3 Share this post Link to post Share on other sites

whitewind Posted July 8, 2013 0.5 is the whole of something, even if it half of something else, as 1 is also a whole and a half (of 2). The question is, can there be an infinite zero? 1 Share this post Link to post Share on other sites

Rabaelthazar Posted July 8, 2013 (edited) but can you actually PROVE that there is no integer between 0 and 1? >>> I Don't think so! Only by the definition of integer being a number from the set {-oo.... -2, -1, 0, 1, 2.....oo}. Although - I think that our mathematical understanding is limited by the fact that our counting system is based on integers. We have a discreet number of fingers, there are a discreet number of apples on the tree etc... and our counting system is based on this. Mathematical constants don't confom to our integer based system, so we either estimate in relation to our integer system (ie: pi can be notated as 3.14..... but will never be completely accurate or use a symbol in place to convey the fact that we can't accurately notate the number using our system. Perhaps there is a counting system we haven't yet discovered, not based on integers, where all the mathematical constants fit perfectly. Maybe? *edited for unclear language Edited July 8, 2013 by Rabaelthazar 1 Share this post Link to post Share on other sites

bullit Posted July 8, 2013 (edited) when a korean is born he/she is 1!!???!! w?? by the way i dont give a fuk if there is a numbar between 0 and 1 <> Edited July 8, 2013 by bullit Share this post Link to post Share on other sites

IndianDreaming Posted July 9, 2013 This might keep you busy trying to work it out: http://en.wikipedia.org/wiki/Principia_Mathematica Share this post Link to post Share on other sites

IndianDreaming Posted July 9, 2013 So Peano naturally assumes that the sequence of integers goes something like dude dude plus one etc but can you actually PROVE that there is no integer between 0 and 1? >>> I Don't think so! Actually in this instance, there's 2 spaces and the letters 'and' between 0 and 1 Share this post Link to post Share on other sites

whitewind Posted July 9, 2013 when a korean is born he/she is 1!!???!! w?? by the way i dont give a fuk if there is a numbar between 0 and 1 <> When a child is born it is already 9 months old. Is 9 months then a true "year" to the human biology, rather than a mere circling of the sun? 1 Share this post Link to post Share on other sites

IndianDreaming Posted July 9, 2013 ^ I hope not! that means I'm over 50!!! Share this post Link to post Share on other sites

CβL Posted July 9, 2013 (edited) The question itself is incompletely-defined. Excluded in the original post, are further rules to define the mathematics at hand (there are probably infinite mathematic rulesets). Is the set of numbers being constructed cyclic, or unbounded? If they're cyclic, then it's a simple matter to show that the cyclic group of numbers with modulus 2.5, and the construction N(n+1) = N(n) + 1 leads to a number between 0 and 1.1, 2, 0.5 (=3 - 2.5) This is not a contrived example, as much as it may seem. We use this type of modular arithmetic to tell the time. Once a time reaches 11:59, it wraps around to 0 again (0 being denoted by the number 12).Now let's assume that we're not using a cyclic group - the group is unbounded. Then in this case, perhaps with a few additional rules (such as to define the notion of 'betweenness'), it is possible to prove there is no natural number between 0 and 1. Making a slapdash definition of betweeness as "A number X is between two other numbers Y and Z, if it greater than only one of Y and Z, and smaller than only the other". X is smaller than Y if X-Y is negative, and X is greater than Y if X-Y is positive.Going by a mathematical induction route:n = 22 - 1 = 1 => 2 is greater than one, 2 is not less than one2 - 0 = 2 => 2 is greater than zero, 2 is not less than zeroThus 2 is not between 0 and 1.Assume that this is true for all positive n. Let's try and prove it for n + 1n + 1 - 1 = n => n + 1 is greater than one, n + 1 is not less than one (as the remainder is n, and n is positive by definition) n + 1 - 0 = n + 1 => n + 1 is greater than zero, n + 1 is not less than zero (as the remainder is n + 1, and it can be shown that n + 1 is positive too, due to the set being unbounded)Thus for all positive integers >= 2, none are between 0 and 1.It can be shown in a similar manner that going to negative numbers will not provide a solution either. So it we can then prove that the set of integers is all the numbers there are in such a system, then we have proved that there is no number between 0 and 1, in this particular system. I think it can be proven that the integers are all the numbers there are with a few more axioms that are usually implicit anyway.So in short, it is the rules of the particular mathematic that determine whether such a question is true or not. There is no one mathematics, but a possibly infinite set of mathematical rulesets, some of which will contain a number between 0 and 1, and others which will not. It is similar to asking "does there exist a penis between the legs of humans" - for some humans it will be true, and for others it will not - we can't provide a binary answer to the question without further specifications. Edited July 9, 2013 by CβL 1 Share this post Link to post Share on other sites

Thelema Posted July 9, 2013 yeah Peano was definitely talking about Z, the set of integers. So I'll restrict my question as pertaining to Z. Share this post Link to post Share on other sites