[Jprogramming] Floor of infinity

[Raul Miller]

The floor of infinity being infinity is not the real problem, opinion.
Or at least not the only problem. And, integer infinity is not a
particularly new concept: https://simple.wikipedia.org/wiki/Aleph_null

Infinity is defined as larger than any number, and larger is not
equal. Or, these sorts of "numeric quality" things can defy logic
because they are not specific values.

But infinity is not the only example of a problem with that
expression.  Consider this:

   (= <.) 0.5+2^128
1

Basically, floating point notation is not capable of representing
large fractional values.

Meanwhile, you could claim that J's implementation of infinity is an
integer infinity (since all values greater than a limit in floating
point notation are integer values).

Anyways, with that out of the way -- what is it that you're trying to
do? And, why is infinity a problem there? And, is this an issue for
you?

   datatype <.2^10
integer
   datatype <.2^100
floating

Thanks,

-- 
Raul

On Sun, Aug 2, 2020 at 2:45 AM Skip Cave <skip at caveconsulting.com> wrote:
>
> I use the (=<.) verb to find integers in a list:
>
>
> * (=<.)1 2.5 2.7 3 4.5 6*
>
> *1 0 0 1 0 1*
>
> * (#~(=<.))1 2.5 2.7 3 4.5 6*
>
> *1 3 6*
>
> I ran across an interesting result when infinity is in the list:
>
> * (=<.)1 2.5 __ 3 4.5 6*
>
> *1 0 1 1 0 1*
>
> * (#~(=<.))1 2.5 __ 3 4.5 6*
>
> *1 __ 3 6*
>
>
> So J is saying that the floor of infinity is infinity (and the ceiling of
> infinity is also infinity). Since infinity is not a number, it would seem
> that an error should be generated when taking the floor of infinity, or
> perhaps NAN, or a zero? In any case, this messes up my nice integer-finding
> verb. Is the\re a mathematical justification for defining the floor of
> infinity to be infinity?
> https://math.stackexchange.com/questions/981708/limit-of-floor-function-when-x-goes-infinity
>
>
> Skip
>
>
> Skip Cave
> Cave Consulting LLC
> ----------------------------------------------------------------------
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