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March 22nd, 2011, 05:56 AM  #1 
Banned Camp Joined: Jun 2010 Posts: 17 Thanks: 0  Maths dont know what a number ismaths ends in meaningless
Mathematicians dont know what a number isthus maths ends in meaninglessness all maths can say is a number is a numberthus the notion of a number is meaningless as we dont know what a number is http://www.scribd.cc/doc/4021/Mathends ... tradiction Mathematicians cannot define a number with out being impredicativeie self referential thus mathematicians dont even know what a number is thus maths is meaningless all maths can say is a number is a numberthus the notion of a number is meaningless http://www.iep.utm.edu/predicat/ In many approaches to the foundations of mathematics, the property N of being a natural number is defined as follows. An object x has the property N just in case x has every property F which is had by zero and is inherited from any number u to its successor u+1. Or in symbols: DefN N(x) ? ?F[F(0) ? ?u(F(u) ? F(u + 1)) ? F(x)] This definition has the nice feature of entailing the principle of mathematical induction, which says that any property F which is had by zero and is inherited from any number u to its successor u+1 is had by every natural number: ?F{F(0) ? ?u(F(u) ? F(u + 1)) ? ?x(N(x) ? F(x))} However, DefN is impredicative because it defines the property N by generalizing over all arithmetical properties, including the one being defined. again impredicative definition Let n be smallest natural number such that every natural number can be written as the sum of at most four cubes. again impredicative definition http://en.wikipedia.org/wiki/Impredicativity Concerning mathematics, an example of an impredicative definition is the smallest number in a set, which is formally defined as: y = min(X) if and only if for all elements x of X, y is less than or equal to x, and y is in X. 
March 22nd, 2011, 07:23 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Maths dont know what a number ismaths ends in meaningle
Be happy!

March 22nd, 2011, 07:33 AM  #3  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Maths dont know what a number ismaths ends in meaningle Quote:
 
March 22nd, 2011, 11:26 AM  #4  
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: Maths dont know what a number ismaths ends in meaningle
In the spirit of a friend of mine who has a tendency to travel beneath bridges just to feed the animals he found there, I glanced through Mr. Dean's paper (the first link). In case you didn't find the time to peruse it, let me sum up my favorite parts: Firstly, 1 + 1 = 1. For example, take two heaps of salt, one on the left and one on the right. Now push them together. Now you get one heap of salt! Secondly, a truly magnificent phrase: Quote:
To be clear, I stand by CRGreathouse  "False."  

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