Re: 176:9 INVALID, -1.0

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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