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Zero to hero (mander.xyz)

submitted 6 months ago by [email protected] to c/[email protected]

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[–] [email protected] 3 points 6 months ago (2 children)

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 ^_^

[–] [email protected] 2 points 6 months ago (2 children)

0 is natural.

Source - programming languages.

[–] [email protected] 4 points 6 months ago (1 children)

*Most programming languages

[–] [email protected] 1 points 6 months ago

We don't talk about those kids, they're weird. :)

[–] [email protected] 2 points 6 months ago* (last edited 6 months ago) (1 children)

I don't personally know many programming languages that provide 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

[–] [email protected] 2 points 6 months ago (1 children)

It's really just a joke about counting from 0 instead of 1.

[–] [email protected] 2 points 6 months ago

Oh, array indexing, sure.

[–] [email protected] 1 points 6 months ago* (last edited 6 months ago) (1 children)

countable infinite set are unique up-to bijection, you can count by rational numbers if you want. I don't think counting is a good intuition.

[–] [email protected] 1 points 6 months ago (1 children)

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.

[–] [email protected] 2 points 6 months ago* (last edited 6 months ago) (1 children)

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? If I am not mistaken, 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.

[–] [email protected] 2 points 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.