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Empirical proof is "dependent on evidence or consequences that are observable by the senses. Empirical data is data that is produced by experiment or observation."

( http://en.wikipedia.org/wiki/Empirical )

"In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true, within the accepted standards of the field. A proof is a logically deduced argument, not an empirical one."

( http://en.wikipedia.org/wiki/Mathematical_proof )

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