# [Gambas-user] Infinities and division

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
>     generally
>     useless.
>
>
> 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.

regards

bruce

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