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March 22nd, 2011, 04:56 AM   #1
bas
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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.
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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.
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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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