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abstract bibtex

abstract bibtex

This paper aims to reestablish the connection between Bolzano's notion of grounding (\\textbackslashem Abfolge\) and (Bolzano's) mathematical practice. Current interpretative literature on Bolzano's notion of grounding analyzes this notion largely in isolation from his mathematical practice, whereas Bolzano himself was interested in grounding first and foremost for the reason that in his view it is fundamental for good mathematical practice. We analyze Bolzano's (1817 and 1833-41) proofs of the theorem that is nowadays known as the Intermediate Value Theorem (IVT) and identify the role of Bolzano's ideas on grounding in these proofs. We will furthermore show that the putative gaps in these proofs can be explained on the basis of Bolzano's ideas on grounding.

@unpublished{ginammi_grounding_0, title = {Grounding in {Bolzano}'s mathematical practice: proofs of the {Intermediate} {Value} {Theorem}}, abstract = {This paper aims to reestablish the connection between Bolzano's notion of grounding (\{{\textbackslash}em Abfolge\}) and (Bolzano's) mathematical practice. Current interpretative literature on Bolzano's notion of grounding analyzes this notion largely in isolation from his mathematical practice, whereas Bolzano himself was interested in grounding first and foremost for the reason that in his view it is fundamental for good mathematical practice. We analyze Bolzano's (1817 and 1833-41) proofs of the theorem that is nowadays known as the Intermediate Value Theorem (IVT) and identify the role of Bolzano's ideas on grounding in these proofs. We will furthermore show that the putative gaps in these proofs can be explained on the basis of Bolzano's ideas on grounding.}, author = {Ginammi, Annapaola and Bellomo?, Anna}, year = {0}, }

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