Metric, of course. The imperial shitload is a bit too large to be practical as it was originally based using only royalty as a benchmark, who have historically had a decided edge in excrement production compared with malnourished peasants. The metric shitload was chosen to accurately represent the average shitload of the common man, and is thus considered to be more accurate in addition to being more egalitarian.
Glad to see somebody here knows the technical term.
“Less exotic” in the sense that they are not anywhere as weird as hyperreals.
“More exotic” in the sense that you won’t find anything about them on wolfram.
Keep in mind that I am a Computer Scientist and these are really for computational purposes (seriously). So I don’t give a dead frog about axioms and such (yet).
OK kind of on the same topic, I recall in grad school talking about “big” infinity vs “small” infinity. Big infinity being infinity^infinity 
It semi-sort-of made sense at the time (can’t remember why to save my ass), not that I’ve ever actually used it in this universe. Has any one ever heard of this or can give a good explanation of same???
Amazing how confusing the factorial symbol can be be when used in normal sentences.
PictsiePat, it looks like you’re talking about cardinalities. The smallest infinite cardinal, omega (also called aleph-naught), is the cardinality of the natural numbers. omega^omega (which is actually the same as 2^omega) is the cardinality of the real numbers, which is strictly larger than omega (in other words, there is no one-to-one correspondence between the set of real numbers and the set of natural numbers, even though both are infinite). We just don’t know how much larger 2^omega is than omega.
Sorry for the hijack, but I was unable to find a thread devoted to this specific topic, and the search engine doesn’t allow the use of quotation marks for an exact phrase.
I’m not sure I understand what’s wrong with this phrase, mostly because I’m not exactly sure what the dictionary definition of “unique” entails. Let me attempt to clarify this: if you have a group of ten teacups, nine white and one pink, within that group, is the pink one unique? If so, why can’t, within a group of nine white teacups and one Chevy Nova, the Chevy Nova be very unique within that group, because, unlike and compared to the pink teacup, it is NOTHING like the white teacups?
Well there is a difference between countable infinite and uncountable infinite. I think.
I was taught that absolutes (like “inifinite,” “perfect,” and “unique”) couldn’t be modified. They were either/or conditions, like “pregnant” or “dead.” You know, you can’t be “a little bit pregnant,” “kinda pregnant,” “partially pregnant;” you either are gravid or not.
Anyone else ever get a similar rule?
Pet peeve time. You shouldn’t use omega for the cardinal because cardinal and ordinal operations, and in particular exponentiation, aren’t the same thing at all. This causes horrible confusion and badness to happen, and makes kittens cry.
In other news, of course ‘almost infinite’ is an imprecise phrase; however it’s quite a useful one because, paradoxically, infinite is often easier to deal with than very large but finite. For example if you have a ludicrously big collection of particles, one might want to approximate them as there being an infinite number of particles, arranged according to some density function. It doesn’t have all the information of the earlier system, but it’s a lot easier to deal with. (Theoretically anyway. Computationally perhaps less so).
Yes, it’s true that cardinal and ordinal exponentiation are different, but it’s not uncommon notation to use 2^omega to denote the cardinal value rather than the ordinal value. Still, it’s a good point to make.
Well, thereby hangs the problem. Unique doesn’t mean “rare”, “unusual”, “bizarre” or even “like, totally freaked-out, man”. It means there’s only one of them. So “rather unique” and “very unique” are plainly nonsense. “Almost unique” scrapes through IMHO - describing a phenomenon which is so rare you could believe it truly unique unless you were erudite enough to know about the one or two other examples that nearly everyone forgets about.
As to freakin’ big numbers, I’ve a soft spot for both moser and Graham’s Number, both of them demonstrably not infinite but so mindbogglingly huge that you can’t represent them with powers, factorials or anything like that.
If I remember High School statistics correctly (which is probably unlikely since my friends and I spent every class of it sitting at the back playing cards), you do that sort of thing with probability models.
Say you’ve got a bag of 8 or so balls. Some are red and some are white. You pick a few random ones. What’s the probability of taking out a certain combination? You can work that out by using a Binomial Distribution model, which is used to model discrete events (the balls you picked) in a discrete space (the bag of 8 balls).
Now say your bag has grown to 6723 balls. You’re still just taking out a few. Now what’s the probability of taking out that combination? You could still use a Binomial Distribution model, but those nifty tables don’t go up to 6723. So what you can do is approximate it using a Poisson Distribution model.
The Poisson Distribution model is normally used to model discrete events in a continuous space, like crashes at an intersection over the space of a year. In fact, a trick we learnt to remember is to recall that ‘poisson’ is French for ‘fish’, and picture a fish (a discrete event) in a fishtank (a continuous body of water). So basically, by modelling a Binomial Distribution with a Poisson Distribution, we are saying that 6723 is “almost infinite” and treating it as it was infinit. I knew my raving would eventually get somewhere…
Okay, so apply this logic to my teacup example. Then the pink teacup WOULD be unique among the white teacups, no? So why CAN’T the Chevy Nova be “very unique” among white teacups when compared to the pink teacup? Noting you said above, by my reading, makes this impossible.
Yeah, it was factorial. It’s a truly enormous, gargantuan, brobdingnagian…Folks, it’s big.
I played around with a symbolic math program and found that 100! has 158 digits, 1000! has 2568 digits, 10000! has 35660 digits. 1000000! has about 5.6 million digits, and I couldn’t find a trick for getting factorials of anything bigger. Notice that the number of digits in the factorial is actually bigger than the number itself. That means 10[sup]20[/sup]! has over 10[sup]20[/sup] digits. You couldn’t store that as a floating-point number using all the memory in all the computers ever manufactured. If you wrote it out longhand with 100 digits to the foot, it would be over 32 light years long.
2[sup]80[/sup]=1208925819614629174706176; only 25 digits. Compared to 10[sup]20[/sup]!, it’s almost infinitesimal :).
But the thing is, we’re not just talking about large numbers here. If we were, I’d win, hands down. We’re talking about numbers that are infinite for all practical purposes, and 2[sup]80[/sup] is good enough for that.
FWIW, log*[sub]10/sub is at most 5, so it’s really not that big at all.
Oh, I agree you can concoct numbers as big as you want. Whatever number you propose, I counter with 10[sup]that number[/sup], or inv log[sup]*[/sup][sub]10[/sub] (that number) or what have you. But the number I gave was an actual quantity that appears in a real calculation that is used every day, the point being that there are indeed practical situations where 2[sup]80[/sup] is nowhere near “almost infinite”.
No, the Chevy’s very unusual, it’s not more unique. There’s only one of 'em in either case.
Having said that, you might I suppose describe something as “doubly unique”, as in, unique for more than one reason: “Fondle’s ‘Triple Concerto in G# Major for nose-flute, washing line and saucepan lid’ is doubly unique: It is the only published work for such an orchestration, and also the only published work in eight sharps.”
Hyperelastic, what kind of wussy number is that where you can estimate how long it would be if it were written out? Go away and come back when you’ve found a really big number! 
No word of a lie; a large computer manufacturer local to me once emblazoned the front of their monthly catalogue with the words:
“With the HyperWarriorSexualViolator PC, the opportunities for entertainment are endless, but not as endless as with the MegaDestroyerDeviantPillager PC”
[sub](OK, I can’t remember what the machines were called, so I made the names up, but the rest is verbatim)[/sub]