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Numbering should start at zero (1982)

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Re: Numbering should start at zero (1982)

#291

Post by jonahx »

pfortuny wrote: post #282
jonahx wrote: post #250

Earlier quoted context omitted.

I don't follow the distinction you're making. The number line is ordered and contains a 0.... The GP's explanation seems more fitting for the year 2000 ambiguity. Are you measuring completed years (celebrate millenium on NYE 2001) or are years the things happening between 0 and 1, 1 and 2, etc (celebrate on 2000, because we're already in the 2000th "gap")?

Order as in "first, second, third", whereas counting is "none, one, two". This is not a formal distinction, it is a conceptual one for things (not mathematical models).

Thought about this a bit more... Not sure if this is what you're saying, but the concept of "space between" I alluded to seems to arise naturally whenever you have ordered items, and vice versa. Because once you have order you have the concepts "greater than"/"less than", and once you have that you have a border between your items, and your items are between those borders. This connects back to Dijkstra's consideration of <, <=, etc....

Re: Numbering should start at zero (1982)

#292

Post by 6yyyyyy »

ufo wrote: post #161

This article is one my pet peeves. It always shows up in discussions as "proof" that 0 indexing is superior, but it hides under the carpet all the cases the where it is not. For instance, backwards iteration needs a "-1" and breaks with unsigned ints. for (i=N-1; i>=0; i--) I like the argument that 0-based is better for offsets and 1-based is better for indexes: https://hisham.hm/2021/01/18/again-on-0-based-vs-1-base…

  for (unsigned i = N - 1; i

Re: Numbering should start at zero (1982)

#293

Post by pfortuny »

jonahx wrote: post #291
pfortuny wrote: post #282

Earlier quoted context omitted.

Order as in "first, second, third", whereas counting is "none, one, two". This is not a formal distinction, it is a conceptual one for things (not mathematical models).

Thought about this a bit more... Not sure if this is what you're saying, but the concept of "space between" I alluded to seems to arise naturally whenever you have ordered items, and vice versa. Because once you have order you have the concepts "greater than"/"less than", and once you have that you have a border between your items, and your items are between those borders. This connects back to Dijkstra's considerati…

Yep, same idea.

Re: Numbering should start at zero (1982)

#294

Post by jacksnipe »

JadeNB wrote: post #286
jacksnipe wrote: post #264

Earlier quoted context omitted.

No, they are axioms. Peano arithmetic itself is a first-order theory, and a theory is just a recursively enumerable set of axioms. Enderton, “A Mathematical Introduction to Logic, 2nd Ed.”, p,203,269-270 Kleene, “Mathematical Logic”, p.206 EDIT: It seems like you're talking about Peano's original historical formulation of arithmetic? That's all well and good but it is categorically not what is meant by "Peano Arithme…

I'm away from my library, but fortunately the books you referenced are a Google away, so I could consult them and confirm that they say what you say. I'm not quite willing to accept Kleene's word as an authority on common modern mathematical practice, since he was a theoretical computer scientist before the term, but, though I'm not familiar with Enderton's book, it certainly looks like a reasonably standard one. But…

It’s not really considered throwing away Peano’s work. Peano was working in the very infancy of logical formalism.

As it turns out, further work developing on his discovered that using a recursively enumerable schema for induction rather than a second-order induction axiom gives rise to a simpler abstraction that still has all the properties that Peano actually desired, and which makes further developments in the space much easier.

Continuing to call it Peano Arithmetic is respect for the fact that the guy got it mostly right, and it took the mathematics community many more years to refine the ideas to their current point.

Is it a shame that Galois theory isn’t presented as a historical fossil and frozen to its state of development in Galois’s lifetime? I may be making a rather big assumption, but I like to think he would be proud, and so would Peano.

Re: Numbering should start at zero (1982)

#295

Post by [deleted] »

c22 wrote: post #259
Brian_K_White wrote: post #202

Earlier quoted context omitted.

I want to be rude. The mix of "The same consideration applies to coordinate systems:" and "r u positioning urself..." in the same message is ridiculous to me and I can't take anyone seriously who speaks like this. It's not illegal or immoral, but it is at the very least, demonstrably distracting from their own actual substantive point. Here we all are talking about that when they otherwise had a perfectly good observ…

Stuff like this could be an innocent attempt to obfuscate one's stylometric fingerprints. I just read around it like mistakes from ESL commenters.

[deleted]

Re: Numbering should start at zero (1982)

#296

Post by amiga386 »

nkrisc wrote: post #170
amiga386 wrote: post #74

Earlier quoted context omitted.

The key word in "birthday" is "birth". Not conception. For human cultural purposes, you are 0 days old at the time and date recorded for your birth. It goes on your birth certificate. If you find a culture that celebrates conceptiondays and issues conception certificates, let me know.

The comment I’m replying said nothing about “birthday”. They asked how many years old you are when you’re born, which is ambiguous. You know some cultures don’t even celebrate birthdays, right? It’s not even uncommon for people to not know their date of birth. Even my own grandmother, born in Chicago in the 1920s, didn’t even know exactly what year she was born in.

When you're born. That is your birth day, because the person to whom you were born gave birth to you that day.

No culture I know of tracks the date of your conception as a measure of your age. If they measure it at all, the starting point is your birth.

You are zero days old on the day of your birth. Even if those cultures think you are "in the first year of your birth" for days 0-365 of your existence, they would accept that 1 day after your birth, you are 1 day old, not 9 months old.

Re: Numbering should start at zero (1982)

#297

Post by [deleted] »

jacksnipe wrote: post #264
JadeNB wrote: post #263

Earlier quoted context omitted.

In the usual terminology, these are not axioms; as your wording itself says, they are definitions. (Indeed, I'd argue that it's almost ungrammatical to say something is "defined in the axioms"; axioms may, and probably must, be stated in terms of definitions, but the definitions are not themselves axioms.) As I say, one can quibble about terminology, since what's important is less what's axiom and what's definition,…

No, they are axioms. Peano arithmetic itself is a first-order theory, and a theory is just a recursively enumerable set of axioms. Enderton, “A Mathematical Introduction to Logic, 2nd Ed.”, p,203,269-270 Kleene, “Mathematical Logic”, p.206 EDIT: It seems like you're talking about Peano's original historical formulation of arithmetic? That's all well and good but it is categorically not what is meant by "Peano Arithme…

[deleted]

Re: Numbering should start at zero (1982)

#298

Post by SideQuark »

nivertech wrote: post #235
feoren wrote: post #192

Earlier quoted context omitted.

> zero represents an absence of quantity and doesn't appear in Nature From one point of view, zero never appearing in nature is exactly an example of it appearing in nature! From another point of view, do you not think a prairie dog has ever asked another prairie dog, "how many foxes are out there now?" with the other looking and replying "None! All clear!"? Crows can count to at least 5, and will count down until th…

> From another point of view, do you not think a prairie dog has ever asked another prairie dog, "how many foxes are out there now?" with the other looking and replying "None! All clear!"? type PrairieDogFoxCount = NoFoxesAllClear | SomeFoxes 1..5 | TooManyFoxes type CrowCount = Some 1..5 | UpsideDown 5..1 type HumanProgrammerCount = 0..MAXINT type HumanMathematicianCount = 0..∞ My point is: "No Foxes - All Clear" is…

> using this definition everything is Natural, including fore example Complex numbers, which is obviously incorrect, and thus invalidates yr argument

Except you’re wrong here; should we thus call your argument “obviously incorrect”?

Complex numbers are natural; they’re fundamental in quantum mechanics. Ever since Schrödinger’s equation fundamentally required them for time evolution of states, physicists (and philosophers) wondered if they could be removed. Recent experiments say “no.” QED and QFTs are the most precise theories known in all of science.

https://physicsworld.com/a/complex-numbers-are-essential-in-...

Re: Numbering should start at zero (1982)

#299

Post by jmkr »

nivertech wrote: post #182
jmkr wrote: post #173

Earlier quoted context omitted.

+1 for peano arithmetic club. I never realized it was controversial. I think I've always included 0 in the nat numbers since learning to count. But there are some programming books I've read, I want to say the Little Typer, or similar, that say "natural number" or "zero". Which makes actually confuses me.

IMO zero represents an absence of quantity and doesn't appear in Nature, so it cannot be classified as a Natural number Just like a negative numbers, it's a higher-level abstraction or a model, not a direct observation from the Nature Likewise, the digit "0" originating from the Hindu-Arabic numeral system[1] is merely a notation, not a number --- 1. https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_s...

A symbol being arbitrary doesn't influence the reality of the meaning behind a thing. I've always thought about `zero` while counting, it never was about `0`.

I observe zero.

I don't think zero is an absence of quantity. I don't think zero is the null set.

You can write types in a programming language, but there are other type theory books that do include zero in the natural numbers. And type theory comes from number/set theory. So it's ok if you decide to exclude it, but this is just as arbitrary.

In fact I'd be happy to write `>=0` or `>0` or `=0` any day instead of mangling the idea of zero representing 0 and zero representing something like `None`, `null` or any other tag of that sort. I don't think the natural world has anything like "nothing" it just has logical fallacies.

Re: Numbering should start at zero (1982)

#300

Post by nivertech »

SideQuark wrote: post #298
nivertech wrote: post #235

Earlier quoted context omitted.

> From another point of view, do you not think a prairie dog has ever asked another prairie dog, "how many foxes are out there now?" with the other looking and replying "None! All clear!"? type PrairieDogFoxCount = NoFoxesAllClear | SomeFoxes 1..5 | TooManyFoxes type CrowCount = Some 1..5 | UpsideDown 5..1 type HumanProgrammerCount = 0..MAXINT type HumanMathematicianCount = 0..∞ My point is: "No Foxes - All Clear" is…

> using this definition everything is Natural, including fore example Complex numbers, which is obviously incorrect, and thus invalidates yr argument Except you’re wrong here; should we thus call your argument “obviously incorrect”? Complex numbers are natural; they’re fundamental in quantum mechanics. Ever since Schrödinger’s equation fundamentally required them for time evolution of states, physicists (and philosop…

No doubt they're useful to explain some theories, but did someone observed in the Nature 6-4i apples or -7+3i particles?
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