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Single Idea 12333

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number ]

Full Idea

There is a heterogeneity of introductory procedures of different classical number types: axiomatic for natural numbers, structural for ordinals, algebraic for negative and rational numbers, topological for reals, mainly geometric for complex numbers.

Gist of Idea

Each type of number has its own characteristic procedure of introduction

Source

Alain Badiou (Briefings on Existence [1998], 11)

Book Ref

Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.125

The 30 ideas from Alain Badiou

12318 The female body, when taken in its entirety, is the Phallus itself [Badiou]
12320 Ontology is (and always has been) Cantorian mathematics [Badiou]
12331 Logic is definitional, but real mathematics is axiomatic [Badiou]
12338 We must either assert or deny any single predicate of any single subject [Badiou]
12332 The modern view of Being comes when we reject numbers as merely successions of One [Badiou]
12337 There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou]
12335 Numbers are for measuring and for calculating (and the two must be consistent) [Badiou]
12334 There is no single unified definition of number [Badiou]
12333 Each type of number has its own characteristic procedure of introduction [Badiou]
12342 Topos theory explains the plurality of possible logics [Badiou]
12341 Logic is a mathematical account of a universe of relations [Badiou]
12340 There is no Being as a whole, because there is no set of all sets [Badiou]
12323 Existence is Being itself, but only as our thought decides it [Badiou]
12321 The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou]
12324 Consensus is the enemy of thought [Badiou]
12322 Must we accept numbers as existing when they no longer consist of units? [Badiou]
12325 Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology [Badiou]
12327 The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou]
12326 The primitive name of Being is the empty set; in a sense, only the empty set 'is' [Badiou]
12329 If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou]
12328 Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou]
12330 In ontology, logic dominated language, until logic was mathematized [Badiou]
12316 For Enlightenment philosophers, God was no longer involved in politics [Badiou]
12317 The God of religion results from an encounter, not from a proof [Badiou]
9808 Philosophy aims to reveal the grandeur of mathematics [Badiou]
9809 Mathematics inscribes being as such [Badiou]
9811 It is of the essence of being to appear [Badiou]
9812 In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]
9813 Mathematics shows that thinking is not confined to the finite [Badiou]
9814 All great poetry is engaged in rivalry with mathematics [Badiou]