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Definitions And Axioms...

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Posted by Mark on July 17, 2003 19:05:17 UTC

Define "Box A" as larger in dimensions and volume than "Box B".

Statement #1: box B is inside box A - possibly but not necessarily. More info needed...

Statement #2: box A is inside box B - FALSE. No more info needed. Impossible by logical consequence of definition.

Box A and box B don't even have to exist for this truth of this concept to be asserted, "statement #2 is false." The truth is platonic as soon as the definition is invented.

Math was both invented and discovered. The definitions and axioms were invented, the subtle truths discovered. That is math...

2 + 2 = 4

"2" defined

"+" defined

"=" defined

"4" defined

"2 + 2 = 4" discovered...

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