Haha, you might have picked the wrong specialty ;)

Do you expect other artists to produce more than one interesting work before you accept that they're good rather than just lucky? Do your arty friends give you blank looks when you say "but how do we know?" You may be applying the scientific method without realising it.

Your questions are interesting, sensible questions with interesting answers. Careers were made by the people who answered them the first time.

Bugger! Catastrophic set hierarchy failure!

Thanks, I'll consider that in the morning and see if I still make any sense.

Remember kids, one little liberal arts paper might seem harmless enough but EVEN ONE can ruin your life.

Identity is an axiom of mathematics. You have to accept it to be doing maths as we understand it, but you're free to examine mathematical systems where a != a and work with the consequences.

Sure, so basically I agree with you. 1/3 is a ratio, and 0.333... is an inconvenient decimal representation of the same. The whole infinity and limits business annoys me when the equivalence between 1/3 and 0.33... is practically speaking a definition and 3*0.33... = 1 is an exercise in misdirection. Since when did real number multiplication involve expanding infinite series? Oh sorry, it has dots on the end. My mistake.

My beef is with the shoehorning of rational numbers into the real space; that ... operator is something you put after a real number to say "only joking! it's not a real number at all, sucker".

</rant>

Sorry to double reply, but there's another way of looking at it I'd like to mention. I might be slightly off on the mathematics (hopefully a kind mathematician will correct me if I mess up) but it might give you another clue about how 0.99... is a special case.

Consider that for any two real numbers x and y, there are an infinite number of other real numbers z where z is between x and y. For a less algebraic example, between 0.1 and 0.2 you have 0.11, 0.12, 0.13, but also 0.111, 0.1111 and so on - an infinite number.

However, between 0.99... and 1.0 there are no more numbers. There's no way to sneak an extra digit on to the back of 0.99... to get another number between it and 1. This is obviously a very special case and for various reasons involving infinity and limits 0.99... and 1.0 are treated/defined as being the same. This might not convince you that they are the same, but hopefully it's easier to see that there's something funky going on with 0.99... even apart from saying that it's the same thing as 1.0.

Well, in base 3, 0.22... == 1.

Briefly, the trick is in the ... operator, it doesn't really work like you'd expect.

(Did I miss something? The parent didn't seem particularly tied to base 10)

An infinitesmial ;)

I think it depends who you ask (I'm not a mathematician, most of my knowledge about this comes from history/philosophy of science).

Although I am a heretic in this matter and shouldn't really weigh in; the ... operator is a mean trick which breaks the laws of arithmetic. That's why you're stumped. It's a shorthand for 'continue to infinity', and as soon as you have an infinity in your equation all bets are off.

The real kicker is that if you're not watching for that sneaky infinity it looks just like a simple equation a five year old can do.

Sorry to reply in an overdone subthread, but I think I have a different objection from the usual.

I'm a programmer, like many here, and I spend a lot of time working with strings, numbers and sequences. I see 0.999... as an infinite sequence which must be partially evaluated when it's used as a number. This has several consequences, but the relevant one is that when comparing numbers the obvious algorithm is to sort them by the greatest non-equal digit - so 0.999... is greater than 0.989..., and must be partially evaluated to determine that 0.9999999... is greater than 0.9999998... This understanding of 0.999... as representing an infinite sequence which can be reasoned about has worked for me in all the situations I've come across (admittedly, not many).

Of course using this reasoning also clearly tells me that trivially 0.999... < 1.

And, before someone asks, I evaluate (1/3) == 0.333... as either true based on no detectable difference, true based on a type conversion from 1/3 being identical to 0.333..., or the heat death of the universe while still looking for an answer.

Now, hopefully something interesting after another "I dun't understand math lol" post.

Obviously the 'correct' interpretation of 0.999... == 1 versus my 0.999...
< 1 is based a difference between 'real' mathematics and the bastardised computer mathematics where we don't actually have infinite sequences and have to make do, but still I can usefully define 0.999... as the largest number which is less than 1 and reason about it on that basis.

So why does 'real' mathematics use a definition based on limits rather than the shortcutty but apparently workable definition I imagine a computer using? Is there some kind of difference based on consistency of the model, or usefulness for some kinds of calculation, or just tradition or what?

P.S., sorry if slashcode ate my less than signs, I think I got them all with &lt;

No, seriously, censorship is when you say something other than your natural inclination due to the expected response from another party.

When Rockstar takes Hot Coffee out of GTA San Andreas because Wal Mart won't carry it with an 18 rating it's censorship.

When you tell your boss "I'm worried that we don't have enough time available to complete the project" instead of "you cockface, we're working 80 hour weeks because you can't project manage for shit and your enormous ego won't let you change the timeline" you're censoring yourself.

Government censorship is merely censorship imposed by the government. There are a million other kinds.

Ah, you bastard! I thought Jimmy had given up his nag campaign now. I feel like I just got goatse'd

The Economist is one of the few publications I will pay to read, and even then I occasionally hit an article where I know some of the background already and the editorial stance smacks me in the face. Still, it is a more reasonable editorial stance than I see anywhere else so I can't really complain. It's just enough to keep me from subscribing.

In other news, I read down the list of options for this poll thinking "hmm... two bucks for a good paper, yep. four bucks for a good paper, yep, ten bucks a month for a good paper, yep... wait a minute, I've never seen what I'd consider a good paper, online or otherwise." </humbug>

Speaking from knowledge of search engine indexing; you can't search on regular expressions because the search index is heavily heavily optimised and the only way to search for a regex would be to generate all the possible expansions and search for them individually. You could do it, it would just fuck up everyone's processes.

If you've done anything with SQL think about how slow wildcard text searches are compared to an indexed primary key search, then multiply by a couple of orders of magnitude since search engines throw away generality for extreme performance on a particular kind of search.

I've recently been trying to do something similar in C# (the other Java), and that syntax would be really handy.

For instance, pulling values out of an XML object if you want parent.element("person").element("addresses").element("work").element("line3").Value ... but when the XML was parsed the person might not have any addresses, a word addres, or whatever is meant to be on line3. You have to check each level individually for null, which is a damn lot of code for nothing useful, or you write a helper function which either returns the final value or null if any of the hierarchy is null.

They've just put that in the language directly, which is fine by me.

Do I have to do everything for you?

without making any value judgement, 117 male births for every 100 female probably isn't chance.