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[Ozle]

Apart from the registration, how many bot style postings do we have though?
Unless they are all setting themselves up for a big push....

A lot of the advertising 'bots' I come across these days are actual real people, who can obviously get through the obvious.

[Drab Emordnilap]

How to you refer to Cities when no piles are empty, when 1 pile is empty, and when 2 piles are empty?

In the past I usually just said "boomtown," regardless of the number of empty piles. If I wanted to refer to the number of empty piles I said how many, or something like "they didn't get going" or "the Menageries ran out," you know. I mean the empty pile may well be part of this story.

Okay I am looking through old posts on the secret forums. In one place onigame says "+2/+2;" in another Locus says "at max;" and once I say "super Boomtowns." Every other place the number of empty piles was either spelled out or not mentioned.

So, if we're your role models, and you decide against spelling it out, there's no special term to let you know it hasn't upgraded, but with one empty pile it's +2/+2 and with two it's max or super.

[TWoos]

I'm not a coder, but as a mathematician I know that you should start counting from 0

That depends on whether you think the natural numbers begin at 1 or 0.

For the purposes of the Well Ordering Principle (WOP), most textbooks start the natural numbers at 1.


Being a coder as well as a mathematician, I still vote for starting City at 0.

[SirPeebles]

I'm not a coder, but as a mathematician I know that you should start counting from 0

That depends on whether you think the natural numbers begin at 1 or 0.

For the purposes of the Well Ordering Principle (WOP), most textbooks start the natural numbers at 1.


Being a coder as well as a mathematician, I still vote for starting City at 0.

Do you really think most textbooks start at 1?  Whenever I've taught those classes, we've started with 0.  When you build your set-theoretic model, you begin with the empty set as zero, and then define the successor operation as Sx = {x}.

[heron]

My textbooks have always started then natural numbers at one, and I've never heard any of my teachers mention that there are other possibilities.

So I guess in my school system, the natural numbers really do always start at one.

I like it that way because then we can have a difference between natural and whole numbers.

[Watno]

Ever heard of negative numbers?

[Tables]

Ever heard of negative numbers?

I think we can all agree that's quite unnatural.

[SirPeebles]

In practice, it doesn't matter if you include 0 as a natural number of not.  In pretty much any theorem, either it doesn't matter or it is evident from context whether 0 must be included or excluded.  But it's important to keep in mind that there is no accepted convention.  I still mention in just about every paper I write what my convention will be for the natural numbers.  Often I write it as $\mathbb{N}_0$ just to avoid confusion.

[Tables]

I've gotten into the habit of specifying whether my Natural numbers are starting at 1 or 0, because about half of my lecturers assume 0 and half assume 1 (note I'm in the UK, so they're all researchers & doctorates, and some are professors - so if there was some universal standard, they'd almost certainly be applying it). Most of them also point out, standards vary, with generally only the incompetent ones assuming it must be 0 or 1 and marking you down for using the other.

[florrat]

In practice, it doesn't matter if you include 0 as a natural number of not.  In pretty much any theorem, either it doesn't matter or it is evident from context whether 0 must be included or excluded.  But it's important to keep in mind that there is no accepted convention.  I still mention in just about every paper I write what my convention will be for the natural numbers.  Often I write it as $\mathbb{N}_0$ just to avoid confusion.

The notation $\mathbb{N}_0$ is just as confusing as  $\mathbb{N}$. I've seen books where  $\mathbb{N}$ excludes 0, and then $\mathbb{N}_0$ contains 0, but also the other way around: $\mathbb{N}$ contains 0, but $\mathbb{N}_0$ does not.

When you build your set-theoretic model, you begin with the empty set as zero, and then define the successor operation as Sx = {x}.

Usually (at least what I've seen) you define Sx = x\cup{x}, especially if you extend the natural numbers to ordinal numbers. This definition is more natural, because then the cardinality of a natural number n is n, and n<m becomes equivalent to n \in m.

[SirPeebles]

Ha, whoops.  Yeah, I meant to say x \cup {x}.

You've seen N_0 not include 0?  What was the context for that?  I have at times used $\mathbb{Z}_{\ge 0}$, but that looks a bit cumbersome to me.  I only used it because $\mathbb{R}_{\ge 0}$ also appeared, and I want to use analogous notation.

[enfynet]

Ever heard of negative numbers?

I think we can all agree that's quite unnatural.

Well they are rooted by imaginary numbers. And everyone knows that something can't be real and imaginary. (except my friends... Those are both)

[Tables]

The most fun is when the lecturer writes N(sub)>0, but the >0 is so small you can't tell if it's a greater or equal, or a greater, and you're doing something just a little too out of reach for you to know immediately which makes sense.

[florrat]

You've seen N_0 not include 0?  What was the context for that?  I have at times used $\mathbb{Z}_{\ge 0}$, but that looks a bit cumbersome to me.  I only used it because $\mathbb{R}_{\ge 0}$ also appeared, and I want to use analogous notation.

It were lecture notes where N was defined to include 0, and they also needed some symbol for N without 0, so they used N_0 for that...
I prefer to write Z_{\geq0} and Z_{>0}, because these notations have an obvious meaning which is the same for everyone (and it's just 1 symbol more than N_0).

[carstimon]

This is how I've seen it split:
If you're interested in the natural numbers themselves (e.g. you're studying set theory or category theory) you usually include zero because it's nice to have an identity for addition.
If you're just using the natural numbers to count/index things you don't include zero.

So usually people using analysis don't include zero and everyone else does.

[TWoos]

I'm not a coder, but as a mathematician I know that you should start counting from 0

That depends on whether you think the natural numbers begin at 1 or 0.

For the purposes of the Well Ordering Principle (WOP), most textbooks start the natural numbers at 1.


Being a coder as well as a mathematician, I still vote for starting City at 0.

Do you really think most textbooks start at 1?  Whenever I've taught those classes, we've started with 0.  When you build your set-theoretic model, you begin with the empty set as zero, and then define the successor operation as Sx = {x}.

I'll concede that I haven't read any sort of majority of textbooks, so I should not have said most.

Instead, I'll say that every single advanced mathematical textbook I've ever used starts the natural numbers at one.

[TWoos]

Ever heard of negative numbers?

Negative numbers aren't natural.

[Watno]

I know, it was a response to this

I like it that way because then we can have a difference between natural and whole numbers.

Even when we do include zero as a natural number, we have a difference between whole numbers and natural numbers.

[GendoIkari]

I just found out my wife is a 0/1/2er.... I think I'll be able to get past it; I'm just worried about how we're going to bring up our children some day!

[heron]

I know, it was a response to this

I like it that way because then we can have a difference between natural and whole numbers.

Even when we do include zero as a natural number, we have a difference between whole numbers and natural numbers.

What's the difference?

[Watno]

{-1, -2, -3,...}?

[TWoos]

I know, it was a response to this

I like it that way because then we can have a difference between natural and whole numbers.

Even when we do include zero as a natural number, we have a difference between whole numbers and natural numbers.

What's the difference?

The definition of Natural numbers is either starting with 0 or 1 and going up.  Two possible meanings, but I'd argue it is still well defined.

The definition of Whole numbers can be either one of those, or it can include negative numbers too.  The problem is that the word Integer is taken from Latin, where it means whole.  So Whole numbers are not well defined.

[Watno]

I never heard of whole numbers not including negatives, but that might be a language thing.

[Polk5440]

I never heard of whole numbers not including negatives.

This has got to be a regional thing. I have never heard anyone include negative numbers in the whole numbers.

[Tables]

Whole Numbers isn't really a term you use in a context where it really matters. As in, you start using Integers/Naturals etc. and stop using Whole Numbers before you start coming across areas of maths where you care about the distinction.