[Gambas-user] Infinities and division
adamnt42 at gmail.com
Tue Nov 29 23:59:52 CET 2022
On 30/11/22 9:01 am, Jussi Lahtinen wrote:
> Mathematically, from the "Infinite Hotel" story,
> infinity <> infinity.
> No, in Hilbert's hotel there is only one sized infinity (countably
> infinite set, example natural numbers and integers).
> It just demonstrates the counterintuitive property of it. However
> there are different sizes of infinity, for example the set of real
> numbers is uncountably infinite. IE set of integers and set of real
> numbers are different in size, but set of integers and set of natural
> numbers are the same size.
Oh, OK. I don't really understand it as I said.
> But, in Gambas
> +Inf = +Inf
> should be true as +Inf is not really "infinity", It's a constant
> representing "a very big number". Otherwise, the constant is
> Yes, that is true as it is the same constant in both sides of the
> equation. However that does not correspond to the mathematical concept
> (it's not a number) of infinity.
> And it should not be used in arithmetics, only for some conditionals
> if at all.
No, I think we do need some arithmetics:
If ( +-Inf + X ) = +Inf = ' -> true, no matter if X is real or natural
but if X = +Inf?
If ( +-Inf - X ) = +-Inf ' -> true, no matter if X is real or natural
but if X = +-Inf?
if ( +-Inf * X ) = +-Inf '-> true, no matter if X is real or natural,
and possibly if X = +-Inf
if ( +-Inf / X ) '-> "Improper Infinites Error"
If ( X / +-Inf ) '-> "Improper Infinites Error"
If ( +-Inf ^ X ) '-> I dont know
if ( X ^ = +-Inf ) '-> I dont know
and there are some debatable points such as -Inf + +Inf hinted at above.
There may be others, Sin(+-Inf)? etc and why btw does Tan(Rad(90))
return 1.63312393531954E+16 ?
I also note that CInt( +-Inf) does return a valid integer, which is fine
and good for my current purposes.
This topic is bigger than I thought.
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