Comment

HexesofVexes@lemmy.world ⁨6⁩ ⁨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 ^_^

source

Sort:hotnew top

Maggoty@lemmy.world ⁨6⁩ ⁨months⁩ ago
0 is natural.

Source - programming languages.

source
- mnemonicmonkeys@sh.itjust.works ⁨6⁩ ⁨months⁩ ago
  *Most programming languages
  
  source
  - Maggoty@lemmy.world ⁨6⁩ ⁨months⁩ ago
    We don’t talk about those kids, they’re weird. :)
    
    source
- baseless_discourse@mander.xyz ⁨6⁩ ⁨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
  
  source
  - Maggoty@lemmy.world ⁨6⁩ ⁨months⁩ ago
    It’s really just a joke about counting from 0 instead of 1.
    
    source
    baseless_discourse@mander.xyz ⁨6⁩ ⁨months⁩ ago
    Oh, array indexing, sure.
    
    source
baseless_discourse@mander.xyz ⁨6⁩ ⁨months⁩ ago
countable infinite set are unique up-to bijection, you can count by rational numbers if you want, it doesn’t matter.

source
- HexesofVexes@lemmy.world ⁨6⁩ ⁨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.
  
  source
  - baseless_discourse@mander.xyz ⁨6⁩ ⁨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.
    
    source
    HexesofVexes@lemmy.world ⁨6⁩ ⁨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.
    
    source