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The book is divided into two parts, with the first exploring notions leading to concepts of actual infinity, concrete but infinite mathematical values. After an exploration of number systems , this part discusses set theory , cardinal numbers , and ordinal numbers , transfinite arithmetic , and the existence of different infinite sizes of sets.
For example, class 5 is defined to include numbers between 10 10 10 10 6 and 10 10 10 10 10 6, which are numbers where X becomes humanly indistinguishable from X 2 [14] (taking iterated logarithms of such X yields indistinguishibility firstly between log(X) and 2log(X), secondly between log(log(X)) and 1+log(log(X)), and finally an extremely ...
The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. [1]
The book includes some irrational numbers below 10 but concentrates on integers, and has an entry for every integer up to 42. The final entry is for Graham's number. In addition to the dictionary itself, the book includes a list of mathematicians in chronological sequence (all born before 1890), a short glossary, and a brief bibliography.
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In this notation, powers of ten are expressed as 10 with a numeric superscript, e.g. "The X-ray emission of the radio galaxy is 1.3 × 10 45 joules." When a number such as 10 45 needs to be referred to in words, it is simply read out as "ten to the forty-fifth" or "ten to the forty-five". This is easier to say and less ambiguous than ...
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