From: Anton Cox (A.G.Cox_at_city.ac.uk)
Date: Thu Feb 07 2002 - 09:28:54 PST
On Thu, 7 Feb 2002, Alan Riddell wrote: > I am not so sure for numbers 0,1,2,3,4,5,6,7,8,9 it is imposiible to tell if > you are using them in a base 10 or higher. The same goes for "Zero", "One", > "Two". You can never tell (just from the string) what base a string of digits is written in. So in each rule we assume (as we are told future rules will use base 11) that they use base 11 - until we can derive a contradiction from this (at which point we rule them invalid). The same does not go for zero, one, two, etc., because they are not written in a basis. They are basis independent. > What would you read 2,007,854 as in base 7? "two double zero seven eight five four". Just as I read telephone numbers out in digits. This is precisely because the phrase "two million, seven thousand, eight hundred and fifty four" is unambiguous because it is not written in a base. Number words describe either parts of numbers (eg as digits in the first reading) or entire numbers (in the second). They are not base dependant as words in either case. Otherwise they would be useless as we would never know what they meant. The phrase "ten is represented in base nine as 11" has content because ten is not a word that depends on the base we use. (Anyway, the restriction in rule one is to "***Write*** all numbers in base 11" (my emphasis).) > Another issue with 1 and 0. Even when working in groups or rings 0 is > sometimes written as the additive identity and is refered to as "the zero" > of the ring. Similarly for 1. Yes, but so what? I have already pointed out that because a word/symbol refers to an object does not mean that it shares the same properties as all other words/symbols that refer to the same object. Twelve and 11 refer to the same number in this round, but only one of them is written in base 11! Best Wishes, Anton -- Rule Date: 2002-02-07 17:28:34 GMT
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