New Infinitary Mathematics
- Sprog:
- Engelsk
- ISBN:
- 9788024646633
- Indbinding:
- Paperback
- Sideantal:
- 352
- Udgivet:
- 19. april 2023
- Størrelse:
- 168x21x233 mm.
- Vægt:
- 574 g.
- Ukendt - mangler pt..
Normalpris
Abonnementspris
- Rabat på køb af fysiske bøger
- 1 valgfrit digitalt ugeblad
- 20 timers lytning og læsning
- Adgang til 70.000+ titler
- Ingen binding
Abonnementet koster 75 kr./md.
Ingen binding og kan opsiges når som helst.
- 1 valgfrit digitalt ugeblad
- 20 timers lytning og læsning
- Adgang til 70.000+ titler
- Ingen binding
Abonnementet koster 75 kr./md.
Ingen binding og kan opsiges når som helst.
Beskrivelse af New Infinitary Mathematics
A rethinking of Cantor and infinitary mathematics by the creator of VopÄ¿nka's principle.  The dominant current of twentieth-century mathematics relies on Georg Cantorâ¿s classical theory of infinite sets, which in turn relies on the assumption of the existence of the set of all natural numbers, the only justification for whichâ¿a theological justificationâ¿is usually concealed and pushed into the background. This book surveys the theological background, emergence, and development of classical set theory, warning us about the dangers implicit in the construction of set theory, and presents an argument about the absurdity of the assumption of the existence of the set of all natural numbers. It instead proposes and develops a new infinitary mathematics driven by a cautious effort to transcend the horizon bounding the ancient geometric world and mathematics prior to set theory, while allowing mathematics to correspond more closely to the real world surrounding us. Finally, it discusses real numbers and demonstrates how, within a new infinitary mathematics, calculus can be rehabilitated in its original form employing infinitesimals.
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