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About ElvargII

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    Goblin Armour

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    Where I am.
  1. Most games will never help you in life but millions of people play those for hours a day. I just found it an interesting aside and it's irritating when people think there is a finite amount of numbers between any two given values, but whatever; I've said pretty much everything I have to say here.
  2. Uh, sorry for having an active interest in mathematics and reading through valid proofs of the various arguments proposed by Georg Cantor and only getting the material I used there from Wikipedia because I was on a time constraint and I knew the majority of people here couldn't care less about cardinality? FYI, it's not copy-pasted and I understand every word, thanks: I followed the structure because, as I said above, most people here couldn't give two [cabbage]s about the stuff and I was on a time constraint. Hell, I tried to make the material as informal as possible so people could easily understand it without Googling away for the next three hours. Whatever; all I was trying to do was shed some light on an interesting topic.
  3. There are no instances of, "Well, it means this to me!" here: these are facts. Look at it this way (yes, I'm going to lift the argument pretty much verbatim from Wikipedia). In mathematics there exists a construct known as a set, and a whole branch of mathematics has evolved around this construct: set theory. A set is a simple thing, really: it's just a collection of objects. For example, {1,2,3} is a set, as is {6,15,415,3.1415926} or {x,y,z}. It seems intuitively obvious that each set has a size: for example, the first and last sets above have three elements, and the second has four. The set {4,7,2,6,2} has five and {} has none.. The size of a set is called its cardinality. Now, think about the natural numbers (the positive integers 1, 2, 3, ...). Can these be expressed in a set? Sure they can: {1, 2, 3, ...}. It's immediately obvious that we cannot list all of the natural numbers and have to condense them as shown: there are infinitely many! For a set with infinitely many elements, does it make sense to talk about its cardinality? The answer is yes. However, we need to extend our number systems to cope with this and this formed the cardinal numbers. The smallest cardinal number is , 'Aleph-null'. is the cardinality of set of natural numbers. Now, think about the real numbers. How many real numbers are there? You might say, "If the cardinality of the natural numbers is and the set of real numbers is infinite too, then there must be real numbers!", but you would be wrong. For each real number, there is an infinite decimal expansion. For example: 1/3 = 0.3333333333... Pi = 3.1415926... 1/2 = 0.5000000000... The digits of the expansion are in a one to one correspondence with the natural numbers: each digit describes one and only one natural number, and that natural number describes that digit only. We know that the cardinality of the natural numbers is , so each expansion has digits. This is true regardless of the mathematical base used, and the argument is simplest in base 2: binary. Each digit of the expansion must be a 0 or a 1, and there are digits. This means that there 2^ ways to fill the expansion. This number is aleph-1. It can be proved that < aleph-1, but I'm running short on time -- look it up yourself if you're interested. The point is that while there are infinitely many real numbers and infinitely many natural numbers, there are 'more' real numbers than there are natural numbers. You can count forever between 1 and 2, but you will never cover all numbers in between them.
  4. Yeah, in set theory there exist different 'sizes' of infinity (hence my Cantor comment a few pages ago). The cardinality of the natural numbers is , for example, and the cardinality of the real numbers is 2^ = . What people almost always mean by infinity in an informal or -- very often -- a scientific context is the definition in real analysis which is infinity as an unbounded limit (to put it loosely, a number larger than every other number) so it's easier to assume that definition unless context dictates otherwise.
  5. aaaaaaaaaaaaaaaaa Yes, , but . The numbers are different depending on whether x increases towards 0 or decreases towards 0; the limit is not equal on both sides. Sure, you could go ahead and create an 'unsigned' infinity and use the real projective line, but since this isn't a field division doesn't even keep the meaning that you're probably familiar with in it. (forgive the dodgy Latex; it's the first thing Google spat out)
  6. The fact that a the result of the division gets arbitrarily large as the divisor gets arbitrarily close to 0 is not the same thing as the division being possible, i.e. the limit as x goes to 0 of 1/x is infinity but the actual division is impossible.
  7. But what size of infinity are we talking about here? Go, Cantor, go!
  8. Try installing / reinstalling the latest drivers available for your card, checking the temperature and reseating the card; I had a similar issue that reseating fixed.
  9. Special variants of the corrupted dragon items are what he's referring to, I'd assume.
  10. Can probably be handwaved away as either a corruption of the original dragons (or using the fantasy favourite of giving it incomprehensibly vast cosmic powers).
  11. Combat's not perfect, but non-combat skills really do need updating. More 'fusion' between the various skills, such as various nontradable items that can only be made with high levels in many non-combat skills would be nice, though some lower level multi-skill items would be nice to complement these. As I've said before, high-level content is all very well and good, some might say that it gives lower levels something to strive for, but training skills becomes very boring very quickly. These multi-skill items could help alleviate that, providing faster / more entertaining ways to train. Of course, some novelty items among them would be good but the multi-skill items provide a somewhat believable base to aid the training of skills.
  12. This is pretty (no, very) trivial, but the mad spirit saying the object was blue probably only refers to the ownership and not the actual colour. Think of the Red Scare -- they weren't scared of people who were actually coloured red. The 'eye' part could just as easily be more symbolism as opposed to referring to the physical shape of the stone. I'm almost certain that it was at one stage called the Fist of Guthix, hence the minigame, yet the indentation in the floor of the arena is consistent with the shape of the stone we are familiar with and not a fist. The idea about the Wilderness being created with Zamorak's attack on Saradomin for the stone is certainly valid. It's certain that the stone was housed in the Fist of Guthix arena for some time, and the Saradominist architecture around the facility could date back to when he had control of the stone and held it there. As a point of interest, does anybody know how the GWD was frozen? Was it a freak accident or deliberately arranged? I don't really want to say anything on that until I know one way or the other. I'm kind of tempted to go for the latter, given the presence of such a powerful weapon and the frozen door; one party in the Third Age could have tried to arrange the preservation of the weapon, and possibly whatever's behind the frozen door, by having the entire dungeon frozen, though why Guthix let this slide is beyond me. If the former is true, then it probably wouldn't really qualify as the last battle of the God Wars: they were effectively ended when Guthix awoke and the freak freezing and recent thawing of one battle is simply a curiosity. If the freezing was deliberately arranged, I'd still lean towards saying it wasn't the last battle but I suppose that they there would be some ground to say that they still continue. (Sorry if I've restated what's already been said or not taken into account other's discoveries. I don't have time to read the entire thread and look through the game for hints at the moment. Hell, even if I had the time to I couldn't look through the game since I have no current membership and am using a laptop with a version of Linux that doesn't support my graphics card well, which has even SD lagging intolerably.)
  13. No idea if this is true (we really need a way to replay quests) but it still doesn't say anything about Saradomin following Armadyl. I think I read something about him being loosely allied with him during the Third Age, but nothing about following him.
  14. And yet, I don't see an Eszett (ß). Haha, kidding -- great job, though I have to wonder where you found the time for all that. :shock:
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