Titlebook: Alice in Numberland; A Students’ Guide to John Baylis,Rod Haggarty Textbook 1988Latest edition John Baylis and Rod Haggarty 1988 Alice.Area

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,Axioms for ℝ—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!

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,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.

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,Psychomotorische Erregungszustände,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.

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,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.