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Posted by Mark on September 1, 2001 22:47:32 UTC

We can't just make bold assertions based off of the definition you gave above for a prime number. If that were the case then there would be no necessity for proof in mathematics; every theorem would be based upon "leap of faith" reasoning.

If a prime number is: "an integer that can only be divided evenly by 1 and itself"......then how can we make the leap to, "2 is the only even prime number"...? At first such a statement would seem self evident, but the fact of the matter is that it relies upon several definitions and axioms. Therefore the assertion that, "2 is the only even prime number"... can hardly be called fundamental. It is a statement that is in fact derived, or in other words "constructed" from a more basic foundation (definitions and axioms). Such an act requires logical proof and this, my friend, is called mathematics. You were correct in stating that definitions decide what it is that is true and not true......and I already have a post waiting for Harv on this one.......but mathematical proof is required to leap from definitions to iron clad theorem. And a mathematical is the work of sound logical reasoning. Now I ask you again.....where does this logic come from and what makes it so valid in our universe?

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