標(biāo)題: Titlebook: Alice in Numberland; A Students’ Guide to John Baylis,Rod Haggarty Textbook 1988Latest edition John Baylis and Rod Haggarty 1988 Alice.Area [打印本頁(yè)] 作者: Taylor 時(shí)間: 2025-3-21 18:14
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作者: 收養(yǎng) 時(shí)間: 2025-3-22 00:18 作者: 蚊子 時(shí)間: 2025-3-22 01:31
,Numbers—in which we abandon logic to achieve understanding, then use logic to deepen understanding, probably of very minor importance initially, being no more than labels to distinguish the verses of ‘one, two, buckle my shoe’, etc. Then they began to have relationships with one another— ‘one’ for some reason always came before ‘two’; and relationships with the outside world— ‘one’, ‘two’, ‘three作者: 生意行為 時(shí)間: 2025-3-22 05:39
,The Real Numbers—in which we find holes in the number line and pay the price for repairs,t takes to get there. What we now need is a working definition of the set ? of rational numbers and a specific interpretation or model of them. Both are easy: the model is the familiar number line in which the rational number . is represented as a distance . along the line from 0, to the left or rig作者: 侵略者 時(shí)間: 2025-3-22 10:01
,Permutations—in which ALICE is transformed,, you lose nothing by skipping this chapter. If at some stage (and exactly which stage doesn’t really matter) you tackle it, we hope you will gain from it an appreciation that many of the concepts discussed in the main stream with reference to numbers are really of much wider applicability. The conc作者: 假 時(shí)間: 2025-3-22 14:58 作者: 是貪求 時(shí)間: 2025-3-22 17:23
,Some Infinite Surprises—in which some wild sets are tamed, and some nearly escape, (1845–1918). Unlike many, perhaps most, major theories in mathematics, Cantor’s ideas on infinite sets owe little to foundations built over previous centuries by other mathematicians. He was the source of most of the ideas, and for this reason the subject is relatively easy to tie down to its origi作者: 忘恩負(fù)義的人 時(shí)間: 2025-3-22 22:21 作者: RENIN 時(shí)間: 2025-3-23 01:26 作者: Chronic 時(shí)間: 2025-3-23 05:57 作者: animated 時(shí)間: 2025-3-23 11:58 作者: Ceramic 時(shí)間: 2025-3-23 15:14 作者: 影響帶來(lái) 時(shí)間: 2025-3-23 22:02 作者: jarring 時(shí)間: 2025-3-24 00:12
,Axioms for ?—in which we invent Arithmetic, Order our numbers and Complete our description of the rs that they are consequences of even more basic assumptions— namely, our axioms. To make the following exposition more palatable, we shall present the defining axioms in three measured helpings. We shall also enlist the aid of our friends Alice, Tweedledee and Tweedledum… so, to work!作者: 廣告 時(shí)間: 2025-3-24 02:40
,The Real Numbers—in which we find holes in the number line and pay the price for repairs,ht, depending on whether . is negative or positive; and our (semi-formal) definition of a rational number is any number which can be expressed as the ratio between two integers, ., with the proviso that m is not zero.作者: licence 時(shí)間: 2025-3-24 07:50
,Psychomotorische Erregungszust?nde,d be no such thing as an infinite set of real objects. However, mathematicians do not, in general, see this as a problem, and confidently assume that infinite sets (even if they are only sets of . objects) can be handled with safety.作者: 樂(lè)章 時(shí)間: 2025-3-24 10:40 作者: LAVE 時(shí)間: 2025-3-24 15:05 作者: scrape 時(shí)間: 2025-3-24 22:33 作者: ASTER 時(shí)間: 2025-3-25 02:03
,Permutations—in which ALICE is transformed,m it an appreciation that many of the concepts discussed in the main stream with reference to numbers are really of much wider applicability. The concepts we have in mind are factorisation, uniqueness, well-defined and equivalence classes.作者: abnegate 時(shí)間: 2025-3-25 03:19
,Some Infinite Surprises—in which some wild sets are tamed, and some nearly escape,centuries by other mathematicians. He was the source of most of the ideas, and for this reason the subject is relatively easy to tie down to its origins. We shall be adding a few remarks to give some historical colour to our story, but by the end of the chapter you will probably agree that the subject is quite colourful enough anyway!作者: Infect 時(shí)間: 2025-3-25 08:06 作者: 欺騙手段 時(shí)間: 2025-3-25 15:06
,Graphs and Continuity—in which we arrange a marriage between Intuition and Rigour,he way space actually is. So far, mathematicians have been able to resolve any unexpected quirks of the rigorously defined concept of a continuous function more or less to everyone’s satisfaction. One of the founders of analysis, a Catholic priest, Bernhard Bolzano (1781–1848 ), when analysing the p作者: 航海太平洋 時(shí)間: 2025-3-25 19:20
http://image.papertrans.cn/a/image/153331.jpg作者: 反應(yīng) 時(shí)間: 2025-3-25 20:28
https://doi.org/10.1007/978-3-540-27243-4: I’ve started to educate myself, Alice, as you suggested. I found a little book in the Red Queen’s library by some chap called Fibonacci. They had very quaint ways of describing themselves in those days: this book was … ‘by Leonardo, the everlasting rabbit breeder of Pisa’.作者: phytochemicals 時(shí)間: 2025-3-26 02:30 作者: CURL 時(shí)間: 2025-3-26 04:49 作者: 類(lèi)人猿 時(shí)間: 2025-3-26 10:34
,Nests—in which the rationals give birth to the reals and the scene is set for arithmetic in ?,Deep in conversation, Alice and the Tweedle twins have wandered into an unfamiliar part of the forest.作者: Adrenal-Glands 時(shí)間: 2025-3-26 13:23 作者: 譏諷 時(shí)間: 2025-3-26 18:17
,Psychomotorische Erregungszust?nde,, 2, 3, 4, …}. We think of counting as a very primitive notion firmly rooted in reality, yet already the innocent three dots in { 1, 2, 3, 4, …} may have taken us beyond reality into the realms of pure thought. The dots are usually interpreted as ‘a(chǎn)nd so on for ever’, which expresses our notion that作者: LAP 時(shí)間: 2025-3-26 23:09 作者: 總 時(shí)間: 2025-3-27 03:03 作者: 無(wú)目標(biāo) 時(shí)間: 2025-3-27 05:40
,Psychomotorische Erregungszust?nde,, you lose nothing by skipping this chapter. If at some stage (and exactly which stage doesn’t really matter) you tackle it, we hope you will gain from it an appreciation that many of the concepts discussed in the main stream with reference to numbers are really of much wider applicability. The conc作者: Leisureliness 時(shí)間: 2025-3-27 11:11 作者: 變形 時(shí)間: 2025-3-27 16:24
https://doi.org/10.1007/978-3-540-27243-4 (1845–1918). Unlike many, perhaps most, major theories in mathematics, Cantor’s ideas on infinite sets owe little to foundations built over previous centuries by other mathematicians. He was the source of most of the ideas, and for this reason the subject is relatively easy to tie down to its origi作者: Eructation 時(shí)間: 2025-3-27 19:57
https://doi.org/10.1007/978-3-540-27243-4ter we shall be investigating limiting processes, the very foundation of analysis. We begin by agreeing that an . is a countably infinite set of real numbers occurring in some definite order, .,.,., …, ., …. Each . .? and there is one . for each .∈?. A favoured abbreviation for a sequence is (. .), 作者: debouch 時(shí)間: 2025-3-28 00:34 作者: Ingest 時(shí)間: 2025-3-28 05:04
Textbook 1988Latest edition...quite the best one I have had the fortune to read... admirable alternative reading for a foundation course introducing university mathematics.‘ David Tall, The Times Higher Educational Supplement作者: 館長(zhǎng) 時(shí)間: 2025-3-28 07:40
https://doi.org/10.1007/978-1-349-09532-2Alice; Area; Factor; Finite; graphs; mathematics; mutation; Permutation; real number; university作者: 兒童 時(shí)間: 2025-3-28 11:03
John Baylis and Rod Haggarty 1988作者: 瘙癢 時(shí)間: 2025-3-28 16:21 作者: Anemia 時(shí)間: 2025-3-28 22:06 作者: Rheumatologist 時(shí)間: 2025-3-29 02:17 作者: 充氣球 時(shí)間: 2025-3-29 03:52
,Alice in Logiland — in which we meet Alice, Tweedledee and Tweedledum, and Logic …,ry one of the brothers tells lies on Mondays, Tuesdays and Wednesdays but tells the truth on the other days of the week. The other brother lies on Thursdays, Fridays and Saturdays but is truthful on the remaining days of the week. One day Alice meets the two in the forest, and the following conversation takes place:作者: 全神貫注于 時(shí)間: 2025-3-29 08:10 作者: VICT 時(shí)間: 2025-3-29 12:17
10樓作者: commute 時(shí)間: 2025-3-29 15:52
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10樓作者: Intersect 時(shí)間: 2025-3-30 00:33
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