0.1

[Chris Torek]

>In article <13983 at mimsy.UUCP> I suggested that
>>If you want to get *really* ridiculous, 0.1 is irrational in irrational
>>bases, but I am not sure those count :-) . 

In article <800 at accelerator> rob at kaa.eng.ohio-state.edu (Rob Carriere) asks:
>You lost me.  How do you do a basis that is not a natural?

Negative integer bases are easy:

	111 base -2  =	1 (-2)^2  +  1 (-2)^1  +  1 (-2)^0
		     =	    4	  +	-2     +      1
		     =	    3

Positive or negative noninteger bases follow the same formula, but
I must admit that inventing a notation for writing fractional digits
is beyond me:

	102 base pi  =  1  pi^2  +  0 pi^1  +  1 pi^0
		     =     pi^2	 +     0    +     1
		    ~=~    10.86960440108935861883449

I have no idea whether fractional and irrational bases are well-regarded
in mathematical circles (mathematical circles are the ones that are *really*
round, rather than the merely arbitrary polygonal CS circles :-) ).
-- 
In-Real-Life: Chris Torek, Univ of MD Comp Sci Dept (+1 301 454 7163)
Domain:	chris at mimsy.umd.edu	Path:	uunet!mimsy!chris