countable infinite set are unique up-to bijection, you can count by rational numbers if you want, it doesn’t matter.
Comment on Zero to hero
HexesofVexes@lemmy.world 7 months ago
N is the set of “counting numbers”.
When you count upwards you start from 1, and go up. However, when you count down you usually end on 0. Surely this means 0 satisfies the definition.
The natural numbers are derived, according to Brouwer, from our intuition of time of time by the way. From this notion, 0 is no strange idea since it marks the moment our intuition first begins ^_^
baseless_discourse@mander.xyz 7 months ago
HexesofVexes@lemmy.world 7 months ago
On the contrary - to be countabley infinite is generally assumed to mean there exists a 1-1 correspondence with N. Though, I freely admit that another set could be used if you assumed it more primitive.
baseless_discourse@mander.xyz 7 months ago
On the contrary - to be countabley infinite is generally assumed to mean there exists a 1-1 correspondence with N.
Isn’t this what I just said? I think, this is exactly what “unique up-to bijection” means.
Anyways, I mean either starting from 1 or 0, they can be used to count in the exactly same way.
HexesofVexes@lemmy.world 7 months ago
I’m arguing from the standpoint that we establish the idea of counting using the naturals - it’s countable if it maps to the naturals, thus the link. Apologies for the lack of clarity.
Maggoty@lemmy.world 7 months ago
0 is natural.
Source - programming languages.
mnemonicmonkeys@sh.itjust.works 7 months ago
*Most programming languages
Maggoty@lemmy.world 7 months ago
We don’t talk about those kids, they’re weird. :)
baseless_discourse@mander.xyz 7 months ago
I don’t personally know much programming language that provides natural number type in their prelude or standard library.
In fact, I can only think of proof assistants, like Lean, Coq, and Agda. Obviously the designer of these languages know a reasonable amount of mathematics to make the correct choice.
(I wouldn’t expect the same from IEEE or W3C, LOL
Maggoty@lemmy.world 7 months ago
It’s really just a joke about counting from 0 instead of 1.
baseless_discourse@mander.xyz 7 months ago
Oh, array indexing, sure.