Infinity [was Re: PEP 526 - var annotations and the spirit of python]

[Steven D'Aprano]

On Wed, 04 Jul 2018 12:31:16 +1000, Chris Angelico wrote:

[...]
>> Ah, I see we're not going to leave it alone.  In that case,
>> "indefinite"
>> is a "number", in that it was a quantity you cited along with the other
>> two. If you'd prefer to call it a "quantity", that's fine with me. 
>> Talk about pedantic...
> 
> I've had debates with people about whether "infinity" is a number or
> not, but I've never yet heard anyone say that "indefinite" is a number.
> Hmm. This could be interesting.

What, haven't you ever raced somebody to see who can count to 100 fastest?

"One, two, skip a few, ninety-nine, one hundred!"

Clearly "indefinite" is just a synonym for "skip a few".


For what it's worth, in the ordinary real numbers we all know and love, 
infinity is absolutely not a number, full stop. There's no debate about 
that.

But there are a number (more than one, less than infinity *wink*) of 
areas of mathematics which treat one or more versions of infinity as 
entities which, for lack of a better name, I'll call "numbers".

E.g. cardinal numbers, hyperreals, surreal numbers, and others.

The mathematics of them is rather unintuitive. For instance, in the 
surreal numbers, ω is the smallest infinity; ω-1 is a separate infinity 
but one that you cannot get by counting up from 0, 1, 2, ... you have to 
start at ω and count down (by subtraction); 1+ω is just ω but ω+1 is 
larger than infinity.


(I'm not an expert on the surreals, I may have a couple of details wrong.)




-- 
Steven D'Aprano
"Ever since I learned about confirmation bias, I've been seeing
it everywhere." -- Jon Ronson