January 9 @Frostgage How often do you go to Gillette Stadium, Fenway Park, and TD Garden? 1 Share this post Link to post Share on other sites Badges

January 9 1 hour ago, ChB said: @Frostgage How often do you go to Gillette Stadium, Fenway Park, and TD Garden? Not very often at all. Too expensive and too many people I'm very content watching at home 1 Share this post Link to post Share on other sites Badges

February 16 On 8/12/2018 at 3:51 AM, Frostgage said: Ants outnumber humans approximately a million to one. (and if they ever figure that out, there goes our way of life!) you are not ready to hear about bacteria On 8/12/2018 at 3:51 AM, Frostgage said: The Fermi Paradox is pretty fascinating. But then anything to do with space and aliens is Paradoxes are usually pretty great too. On 8/12/2018 at 3:51 AM, Frostgage said: The earth is round b a d f r o s t y How's your study been going since I last posted on this thread? What's your favourite number? Which of the 16 pool balls is your favourite? What's your favourite mathematical infinity? 1 Share this post Link to post Share on other sites Badges

February 16 48 minutes ago, Duality said: How's your study been going since I last posted on this thread? What's your favourite number? Which of the 16 pool balls is your favourite? What's your favourite mathematical infinity? 1. It's been very challenging but has gone pretty well. I'm thirsty for that degree so I refuse to give up 2. 97 3. Definitely the 4 ball. Solids > Stripes and it's such a nice shade of purple, which is my favorite color <3 4. The number of characters in the Raildex universe (actually though can you give me some examples?) Edited February 16 by Frostgage 1 Share this post Link to post Share on other sites Badges

Sunday at 02:06 AM 16 hours ago, Frostgage said: It's been very challenging but has gone pretty well. I'm thirsty for that degree so I refuse to give up such a committedfrosty <3 16 hours ago, Frostgage said: 97 Ooh, that's an interesting pick. May I ask why it's your favourite? 16 hours ago, Frostgage said: Definitely the 4 ball. Solids > Stripes and it's such a nice shade of purple, which is my favorite color <3 same o: 16 hours ago, Frostgage said: The number of characters in the Raildex universe (actually though can you give me some examples?) With exceeding pleasure. Click the spoiler at your own risk. Spoiler For starters, there's your standard sideways-eight infinity, mathematically defined along the lines of 'bigger than any finite number', which is mostly just used to signify the end of the number line instead of in any particularly formal capacity. Besides that - in fact the only mathematical infinities I know of besides that one (not that these aren't quite sufficient) -, there are numbers called infinite ordinals and infinite cardinals, which are a quite recent discovery. Cardinals are the numbers used to denote how many members there are in a set (the 'size' of the set), while ordinals are the numbers used to put the members of the set in order (the 'labels' on the members). For example, a set with five members in it (5 here being the cardinal number characterising the set) has a first member, second member, third member, fourth member, and fifth member (1-5 here being the ordinal numbers of the members of the set). For standard finite sets, cardinal numbers are equal to the ordinal number of the final member in the set (in the above set, the cardinal number is 5 and the final member in the set is the fifth and hence has ordinal number 5), so no heed was paid to the difference for very many years. However, a chap called Cantor muddled everyone's heads up in the late 1900s by proving that for infinite sets, cardinal numbers and ordinal numbers behave very differently. The (infinite) set of whole numbers has an (infinite) cardinal number denoted aleph-nought and a final (infinite) ordinal number called omega-nought. If you add one extra number to the set of whole numbers (call the number A), you end up with a set with cardinal number aleph-nought, as before, but A has an ordinal number of omega-nought plus one. That is, the set's size is unchanged, because the new set is just as infinite in size as the original set, but the final ordinal number in the set has gone up by one to reflect the fact that you still need an extra 'label' for A - it has to be the 'omega-nought plus one'th number in the set because the 'omega-nought'th number is still in the same position as it was before. To put this more succinctly, omega-nought plus one is greater than omega-nought, but aleph-nought plus one equals aleph-nought. This is the true resolution to the dilemma of whether infinity plus one is bigger than infinity - it depends on whether the infinity is a cardinal number or an ordinal number. It is notable that omega-nought plus one is a distinct infinite ordinal number in its own right. There are in fact an infinite number of infinite ordinals along these lines, from omega-nought to omega-nought plus one to omega-nought plus two to omega-nought plus a thousand to omega-nought multiplied by two to omega-nought multiplied by a thousand to omega-nought to the power of two to omega-nought to the power of a thousand to omega-nought to the power of omega-nought to omega-nought to the power of omega-nought to the power of omega-nought to omega-nought to the power of omega-nought to the power of omega-nought to the power of omega-nought so on up with an infinite number of omega-noughts stacked as exponents. This ludicrously large number is called epsilon-nought, and it still corresponds with the cardinal number aleph-nought. But the fun doesn't stop there, nosirree. You can continue the procedure of increasing size with epsilon-nought plus one plus two plus three times a thousand and so on all the way up to epsilon-one. After that, as I'm sure you've probably realised already with a sinking feeling in your stomach, you can continue the insanity to result in the even more ludicrous number epsilon-epsilon-epsilon-epsilon-epsilon-etc. right on down the subscripts to max out epsilon notation altogether. This number is called lambda-nought, and it still corresponds to the infinite set cardinal number aleph-nought. You can continue this overarching pattern of omega-nought epsilon-nought lambda-nought even further if your brain isn't half boggled enough to result in what they call the Veblen hierarchy of infinite ordinals, which maxes out at a terrifyingly large number called the Fefermann-Schutte ordinal - again, corresponding with a set of cardinal number aleph-nought. Fortunately no doubt for you, I can't pursue this already quite infinite rabbit hole any further, because the Fefermann-Schutte ordinal is the limit of infinite ordinals that can be expressed along these lines with any sort of symbol notation of finite length. Unfortunately no doubt for you, I haven't even gotten started on omega-one. Note that epsilon-nought was derived from omega-nought to the power of omega-nought so on up, not omega-omega-omega-omega-etc. like how lambda-nought was generated with epsilon-epsilon-epsilon right on down the subscripts. So far we've been talking about infinite ordinals that correspond with a set of cardinal number aleph-nought - that is, a set the same size as the set of whole numbers. However, there are an infinite number of sets with larger cardinal number. Consider, for example, the set of real numbers. This includes 1.5 and 1/3 and pi and e and 0.5342333456464444665652189853 and any weird number you can get from spamming buttonpresses on your numpad. This set is infinite in size - it has an infinite cardinal number (typically called C) -, but it is larger than the set of whole numbers - that is, C > aleph-nought (more specifically, C equals two to the power of aleph-nought). The final (infinite) ordinal number in the set of real numbers is called - you guessed it - omega-one (much, much larger than the Fefermann-Schutte ordinal). You can do all of the same abominations against nature with omega-one and any other omega number as I did last paragraph with omega-nought, just to give you nightmares tonight, but the real fun is in the cardinal numbers now. C is called 'the cardinality of the continuum', and it is the number of points in a line of infinite length (hence why we have the 'number line' with a simple line of infinite length expressing all the real numbers). However, to the dismay of maths students the world over, C is also the number of points in a line of finite length, the number of points in a plane whether finite or infinite, the number of points in a solid of any size, and in fact the number of points in any given geometric 'continuum' (hence the name). Aleph-one, on the other hand, is defined as the smallest infinite cardinal after aleph-nought. Many think, and it would be quite elegant if it were so, that C is equal to aleph-one, but this idea highlights a peculiar quirk in the standard mathematical system most mathematicians work within. Within this system, named ZFC, the theorem that C equals aleph-one is unprovable. This is not to say that it can be disproved, but that the truth of the equation is entirely independent of the system - you can't prove or disprove it without adding additional axioms to the ones that ZFC is founded on. In other words, whether C = aleph-one is entirely up to you, so to speak, so you could consider C and two to the power of C and two to the power of two to the power of C and so on a group of infinities of an entirely different class to the alephs. At any rate, the aleph numbers also form an infinite progression, what with aleph-one and -two and -three and so on up to aleph-omega-nought and beyond (if aleph-one equals C, aleph-two equals two to the power of C and aleph-three equals two to the power of two to the power of C and so on). Each aleph-x number has a corresponding omega-x number that is the smallest possible final label that corresponds with that set size, and you can add and multiply and exponentiate these omega-x numbers to create as many ordinal numbers as you like that are all larger than omega-x but correspond with the same aleph-x. And with that, you are now equipped to decide on your favourite infinity - sideways-eight, a particular aleph number, a particular omega number, a particular epsilon/lambda number, the Fefermann-Schutte ordinal, any given string of ordinal numbers added to and multiplied with and placed to the power of each other (e.g., omega-eighteen to the power of 5.5 times pi plus omega-three to the power of omega-nought to the power of seven times 88 plus the Fefermann-Schutte ordinal times 9.7 plus lambda-four times 0.3 plus epsilon-two to the power of epsilon-nought plus 137), or possibly the C series. EDIT: turns out that sideways-eight is in fact the symbol for the collective metaset/'class' of all ordinal numbers including every single variant on omega numbers i mentioned and all the epsilons and lambdas and the fefermann-schutte ordinal and literally all of the other infinities except the aleph series/c series sideways-eight is op pls nerf What's your favourite physical game? What's your favourite tactical game? What's your favourite digital game? Can I offer you a glass of water after that infinity brainbashing? Edited Sunday at 02:26 AM by Duality 1 Share this post Link to post Share on other sites Badges

Sunday at 06:33 AM 4 hours ago, Duality said: Ooh, that's an interesting pick. May I ask why it's your favourite? It was the first number I was given to wear in baseball. At first it started out as a joke because it's such an awful number (in pro baseball established players wear low numbers) but now I love it lol 4 hours ago, Duality said: With exceeding pleasure. Click the spoiler at your own risk. oh my goodness that Cantor guy basically made "infinity + 1" into a reality xD that's my hero 4 hours ago, Duality said: What's your favourite physical game? What's your favourite tactical game? What's your favourite digital game? Can I offer you a glass of water after that infinity brainbashing? 1. To play = basketball, to watch = U.S. football 2. Scrabble for sure 3. The one and only 4. i don't know, can you? yes please thank you <3 1 Share this post Link to post Share on other sites Badges

Monday at 03:38 AM 16 hours ago, Frostgage said: oh my goodness that Cantor guy basically made "infinity + 1" into a reality xD that's my hero who says you can't change the world with maths 16 hours ago, Frostgage said: To play = basketball, to watch = U.S. football Ah, yes, good old-fashioned 'remove the ball from the possession of the other team and place it into the designated area'. 16 hours ago, Frostgage said: Scrabble for sure The second best usage of a dictionary after pwning people on the internet. What's the most memorable word-scoring you've ever managed to achieve? 16 hours ago, Frostgage said: The one and only t o o m a n y w a i f u s 16 hours ago, Frostgage said: i don't know, can you? yes please thank you <3 you had it right the first time zeno's arguments on the topic of infinity posit that motion is an illusion is it even possible for me to give you a glass of water Spoiler apparently it is possible <3 What's your favourite type of light source? How many dragonflies have you seen in your life? Why is Gamora? What was your first word? 1 Share this post Link to post Share on other sites Badges

Monday at 08:42 PM 16 hours ago, Duality said: Ah, yes, good old-fashioned 'remove the ball from the possession of the other team and place it into the designated area'. Hey they're not all the same. One uses feet (well not really) and the other uses baskets 16 hours ago, Duality said: The second best usage of a dictionary after pwning people on the internet. What's the most memorable word-scoring you've ever managed to achieve? "Centavos" for 167 points 16 hours ago, Duality said: What's your favourite type of light source? How many dragonflies have you seen in your life? Why is Gamora? What was your first word? 1. I know lava lamps aren't really lamps but they're just so cool. I'mma go with that 2. Oh man I used to see those all the time where I lived as a kid but not many since then. I like them because they're one of the few insects that isn't evil hehe 3. We might find out in a couple months <3 End Game HYPE 4. Unfortunately I've forgotten :c Fortunately people have since told me what it was c: Unfortunately I've forgotten that too :c Although one thing I do know is that supposedly I didn't talk until very late (when I was 3 years old) 1 Share this post Link to post Share on other sites Badges

Monday at 10:06 PM 22 minutes ago, Frostgage said: Hey they're not all the same. One uses feet (well not really) and the other uses baskets One involves using feet to remove the ball from the possession of the other team and the other one involves using hands to remove the ball from the possession of the other team. One has small upright baskets as the designated area and the other one has large sideways baskets as the designated area. 26 minutes ago, Frostgage said: "Centavos" for 167 points 27 minutes ago, Frostgage said: I know lava lamps aren't really lamps but they're just so cool. I'mma go with that Perfect choice. 10/10. 28 minutes ago, Frostgage said: We might find out in a couple months <3 End Game HYPE s o o n 28 minutes ago, Frostgage said: Unfortunately I've forgotten :c Fortunately people have since told me what it was c: Unfortunately I've forgotten that too :c Although one thing I do know is that supposedly I didn't talk until very late (when I was 3 years old) mysteriousfrosty What's your favourite letter of any alphabet? How many Frostgages would it take to change a lightbulb? What's the most recent doodle you've drawn? How many microscopic skin mites do you have on your left eyebrow? Share this post Link to post Share on other sites Badges

Tuesday at 09:07 PM 21 hours ago, Duality said: mysteriousfrosty Remember, Einstein didn't talk until he was 4 lol of course that could be one of those myths like people only using 10% of their brain. I dunno 21 hours ago, Duality said: What's your favourite letter of any alphabet? How many Frostgages would it take to change a lightbulb? What's the most recent doodle you've drawn? How many microscopic skin mites do you have on your left eyebrow? 1. Chi from the Greek alphabet. I was one of the few people in my stats class who did really well with the chi-squared distribution and the lowercase letter with the one squiggly diagonal line is so much fun to write <3 2. Hopefully just one. Those other Frostgages are useless anyway 3. I actually don't draw. Like at all. Because I'm not good at it :V 4. nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope 1 Share this post Link to post Share on other sites Badges

2 hours ago 2 hours ago, Frostgage said: Remember, Einstein didn't talk until he was 4 lol of course that could be one of those myths like people only using 10% of their brain. I dunno I looked for a source but all I could find was that Einstein enjoyed reading Kant's Critique of Pure Reason by the age of 13. I've been meaning to read that book for a while now and this is just another reason to. 2 hours ago, Frostgage said: Chi from the Greek alphabet. I was one of the few people in my stats class who did really well with the chi-squared distribution and the lowercase letter with the one squiggly diagonal line is so much fun to write <3 When I Googled the letter to see what it looked like, the phrase 'chi marks the spot' popped into my head, and now my imagination is running rampant with the idea of pirate statisticians who only give probability distributions for the location of their treasure. 2 hours ago, Frostgage said: Hopefully just one. Those other Frostgages are useless anyway the one and only bestfrosty isn't useless though <3 2 hours ago, Frostgage said: I actually don't draw. Like at all. Because I'm not good at it :V You haven't drawn any form of figure that you can recall, including diagrams to help you understand concepts? 2 hours ago, Frostgage said: nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope nope Only 21 of them? That's not many to have in your eyebrow; most people have hundreds if not thousands in total living on their face. What's the niftiest gamepiece or set thereof (dice, playing card, board game board, chesspiece, etc.) that you've ever seen? What's your favourite mathematical constant? What's the heaviest thing you've ever lifted? What's the happiest that you've ever made somebody, and how did you make them that happy? Share this post Link to post Share on other sites Badges