Egyptian-Fraction Expansions Of REALS

[Jud McCranie]

At 09:57 PM 1/20/2004, Leroy Quet wrote:

>If we have a positive REAL, possibly irrational, x,

I like your idea.

>We might want to, in order to be strict with our definition of
>"Egyptian-Fraction", rewrite the "3"  in the pi-expansion as "1+1+1",  to
>get:
>
>pi =  1 + 1 + 1 + 1/8 + 1/61(?) +...

No, don't write it as 1+1+1.  For the sequence, make the first term the 
integer part and continue with the denominators.  For one thing, the 
Egyptians didn't do that.  Secondly, the sequence could start with a very 
long string of 1s.  (Alternatively, skip the integer part altogether.)