2**2**2**2**2 wrong? Bug?

mensanator at aol.com mensanator at aol.com
Fri Jul 13 23:32:03 CEST 2007


On Jul 13, 2:52 pm, Wayne Brehaut <wbreh... at mcsnet.ca> wrote:
> On Fri, 13 Jul 2007 11:30:16 -0700, Paul McGuire <pt... at austin.rr.com>
> wrote:
>
>
>
>
>
> >On Jul 13, 1:20 pm, Wayne Brehaut <wbreh... at mcsnet.ca> wrote:
> >> On Mon, 09 Jul 2007 23:51:25 -0700, "mensana... at aol.com"
>
> >> <mensana... at aol.com> wrote:
> >> >On Jul 9, 11:42?pm, Paul McGuire <p... at austin.rr.com> wrote:
> >> >> On Jul 9, 11:21 pm, "Jim Langston" <tazmas... at rocketmail.com> wrote:> In Python 2.5 on intel, the statement
> >> >> > 2**2**2**2**2
> >> >> > evaluates to>>> 2**2**2**2**2
>
> >> >> > 200352993040684646497907235156025575044782547556975141926501697371089405955  63114
> >> >> > 530895061308809333481010382343429072631818229493821188126688695063647615470  29165
> >> >> > 041871916351587966347219442930927982084309104855990570159318959639524863372  36720
>
> >> >> <snip>
>
> >> >> Exponentiation is right associative, so this is the same as:
>
> >> >> 2**(2**(2**(2**2)))
> >> >> 2**2**2**4
> >> >> 2**2**16
> >> >> 2**65536
>
> >> >> 2=10**0.3010, so 2**65536 is approx 10**19726
>
> >> >> There are 19730 digits in your answer,
>
> >> >>>> import gmpy
> >> >>>> n = 2**2**2**2**2
> >> >>>> gmpy.numdigits(n)
> >> >19729
>
> >> >Did you count the 'L'?
>
> >> numdigits(n)?
>
> >> What?  'L' is a digit in Python?  I'm going back to Fortran!
>
> >> wwwayne
>
> >> >>so this seems to be at least in
> >> >> the ball park.
>
> >> >> -- Paul- Hide quoted text -
>
> >> - Show quoted text -- Hide quoted text -
>
> >> - Show quoted text -
>
> >'L' counts for 50, but only when you use Roman font.
>
> WTL?!  Not Times  New Roman I hope?
>
> Now I'll have to extend my remarks below to include:
>
>         L**L**L
>         D**D**D
>         M**M**M
>         etc. (since I don't recall what comes next)
>
> though these (L, D, M, ...)  would seem to be numbers rather than
> digits: the Romans used a base-1 system

No, "base" refers to a Positional Number system for which
radix 1 is undefined.

You can call Roman Numerals a Tally System of Radix 1.
Tally sytems ARE defined for radix 1, but operate
completely different from positional systems.

> [for purposes of this
> argument, at least] so  I is the only Roman digit* and the others are
> just shorthand for:
>
>    I = 1
>    V = IIIII
>    X = I*10
>    L = I*50
>    D = I*500
>    M = I*1000
>    etc.
>
> ---
> For those who don't know which Roman digit I represents:
>
>    |
> _\|/__
>
> wwwayne
>
>
>
>
>
> >-- Paul




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