[TIB] Fractional Numbers Stumper (re: TI-OS bug)

To: ti-basic@lists.ticalc.org
Subject: [TIB] Fractional Numbers Stumper (re: TI-OS bug)
From: "Arthur J. O'Dwyer" <ajo@andrew.cmu.edu>
Date: Thu, 19 Sep 2002 16:53:19 -0400 (EDT)
In-Reply-To: <20020919193224.916BD181BD@mx-1.sollentuna.net>
Reply-To: ti-basic@lists.ticalc.org



Here's the cause of the TI-83 "bug" that I reported on the 13th.

  Any time you take the integer -1 and divide it by any of
{3,7,9,14,19,22,26,30,33,34,38,43,45,48,49...} or these
numbers' additive inverses {-3,-7...}, and then multiply
back by the same thing you divided by (or its inverse),
you get the "fractional number" -1 (or 1), whose iPart
is 0 and whose fPart is the number -1 (or 1).

[Let's define "fractional numbers" as all numbers X such
that (X=n) returns 1, where n is an integer, and fPart(X)
does not return 0.]

  This weird effect is probably because of the internal
representation of fractions on the TI-83.  [That is, the
fractional number "-1" displayed by the calculator is really
"-0.999999...", but it's treated as equal to "-1" in all
ways except iPart/fPart.]  Does anyone know anything
relevant to this?

  How else are "fractional numbers" distinguishable from
integers?  They have non-zero fPart()s, they produce
INVALID DIM errors when used as list or matrix indices,
...anything else?

  Is there a way to generate "fractional numbers" other
than "-1" and "1"?

 -Arthur

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