| Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA248.SPR. FCT 94846 (Browse shelf) | 1 | Available |
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| QA641.SPR. FCT 94843 Handbook of normal frames and coordinates | QA297.SPR. FCT 94844 Infinite matrices and their finite sections | QA377.SPR. FCT 94845 Qualitative theory of planar differential systems | QA248.SPR. FCT 94846 Axiom of choice | QA274.SPR. FCT 94847 Multidimensional diffusion processes | QA331.5.SPR. FCT 94848 Duality for nonconvex approximation and optimization | QA76.95.SPR. FCT 94851 The mathematica guidebook for numerics |
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AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that: Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC). Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games). Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e.g., by AD, the axiom of determinateness). Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
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