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Replacing objects of mathematics by other objects with the same name

Zbigniew Semadeni — 2007

Didactica Mathematicae

The purpose of the paper is to introduce and analyse the following conception: by an ontic shift X ˜ X ' ' we mean an (explicit or hidden) replacement of a mathematical object X ' called X by a different object X ' ' which is also called X and is to play the role of X ' . If X ' and X ' ' are sets, then X ' X ' ' means that these sets are different in the usual sense. Otherwise X ' and X ' ' may stand for basic concepts of mathematics such as, e.g., point, straight line, natural number, addition of natural numbers, (standard) real...

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