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 March 22nd, 2011, 04:56 AM #1 Banned Camp   Joined: Jun 2010 Posts: 17 Thanks: 0 Maths dont know what a number is-maths ends in meaningless Mathematicians dont know what a number is-thus maths ends in meaninglessness all maths can say is a number is a number-thus 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 impredicative-ie self referential thus mathematicians dont even know what a number is- thus maths is meaningless all maths can say is a number is a number-thus 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: Def-N 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, Def-N 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, 06:23 AM   #2
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Re: Maths dont know what a number is-maths ends in meaningle

Be happy!
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March 22nd, 2011, 06:33 AM   #3
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Re: Maths dont know what a number is-maths ends in meaningle

Quote:
 Originally Posted by bas Mathematicians cannot define a number with out being impredicative
False.

March 22nd, 2011, 10:26 AM   #4
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Re: Maths dont know what a number is-maths 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:
 Originally Posted by Colin Leslie Dean CONTRADICTION, OR INCONSISTENCY WITHIN A VIEW AS WELL AS MUTUAL CONTRADICTION, OR INCOMMENSURABLITY BETWEEN VIEWS DOES NOT PRECLUDE THE VIEW OR BOTH VIEWS FROM BEING ‘TRUE’
I found it highly amusing though, ultimately, a waste of time. To end with another quote, I found myself terrified, mortified, petrified, stupefied... by the Mr. Dean.

To be clear, I stand by CRGreathouse - "False."

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