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Subject: "Is 1+1=2 an axiom?"     Previous Topic | Next Topic
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Conferences The CTK Exchange Middle school Topic #19
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S. H. Kelly
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 Oct-27-00, 01:16 PM (EST)
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"Is 1+1=2 an axiom?"
 
   Axioms are usually considered to be the basic "facts" of a system, such as "Mathematics".

Some consider an axiom to be facts of the system that cannot be
derived from other facts...

Here are my thoughts:

It'seems to me that either axioms CANNOT exist, or that EVERYTHING is an axiom.


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alexb
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672 posts		 Oct-27-00, 01:18 PM (EST)
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1. "RE: Is 1+1=2 an axiom?"
In response to message #0
 
   Yes and no: everything may be an axiom depending on your tastes and inclinations. Usually when one is concerned with an axiomatic system, simplest (in one's judgment) statements are selected to be axioms of that system.

All the best,
Alexander Bogomolny


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JeanMarie
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 Oct-29-00, 08:12 AM (EST)
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2. "RE: Is 1+1=2 an axiom?"
In response to message #0
 
   >Here are my thoughts:
>
>It'seems to me that either
>axioms CANNOT exist, or that
>EVERYTHING is an axiom.

To say that axioms can't exist is like saying that you can build a house in the air or play a game without defining a rule first.

To say that everything is an axiom means that all the genius that build the mathematics by demonstrating theorems lost their time. If the theorem that the sum of the angles of a triangle equals 180° becomes an axiom, how would it be better than another axioms saying it is 181° ?

The first part of you sentence makes thinking impossible and the second one forbids it. Why do you hate so much intelligence ?

Jean-Marie


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