{"product_id":"9783540309895","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eHerrlich, Horst\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eAC, 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:\u003c\/p\u003e\n\u003col\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003c\/ol\u003e\n\u003cp\u003e- Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC).\u003c\/p\u003e\n\u003col\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003c\/ol\u003e\n\u003cp\u003e- Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games).\u003c\/p\u003e\n\u003col\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003c\/ol\u003e\n\u003cp\u003e- Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e.g., by AD, the axiom of determinateness).\u003c\/p\u003e\n\u003col\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003c\/ol\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003eIlluminating 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2006-05-11\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540309895\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/11601562\u003c\/p\u003e \u003cp\u003eDimensions: 233cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 198\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":45369684263052,"sku":"9783540309895","price":58.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540309895.jpg?v=1775673686","url":"https:\/\/lateknightbooks.com\/products\/9783540309895","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}