Comment by ysofunny | Hacker News Reader

Comment by ysofunny | Hacker News Reader

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> There’s a very deep problem with that—every time you invent a “superset”, do you then have to redefine the subset to be a subset of that “superset”?

I have thought about this too, and I'd initially agree with you. but I thought at some point how mathematical history is not extremely dissimilar from this. put in very rough terms:

at first humans discovered/invented numbers (i.e. the counting numbers); these started at number one — the first number. later on, at some point we had to go back and realize that there was a zero before number one which "silently" redefined the first number as zero and this created the natural numbers a the modern set-based N

edit: adding this alternative rendering of my intended comment triggered by a condescending reply: "mathematics silently redefines stuff all the time. deal with it"

There is a different answer here which is more satisfactory… which is to use notions of equality other than set theoretic equality. Which is what the article is talking about.

I have the naive feeling that early counting may have included 0 as a primitive right from the get-go. The need to say "nothing" seems pretty primal.

Zero entered western writing systems through India, with limited usage in math before that. It seems like it was invented/borrowed as part of switching from additive numbers (such as Roman numerals) to positional numbers.

"Nothing" as a concept always existed of course. But it wasn't considered a number, generally. Certainly no one counted "nothing, one, two", and even today natural language doesn't include "nothing" or some equivalent as a numeral noun.

You need to be careful about the phrase “considered a number” since I believe one, or unity, was also not considered a number by some ancient civilisation - i.e. a number was only multiple copies of unity.

[I believe this YouTube video goes into more detail in its discussion of why 1 was not considered Prime in the ancient world: https://youtu.be/R33RoMO6xeA]

That's where I'm quite skeptical. Imagine you are in charge of trade or rationing important village resources in the winter. It just seems to me almost necessary that people would have a way to symbolically indicate that all the sheep are gone. As opposed to just not having any symbol for that at all.

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