=== ANCHOR POEM === ════════════════════════════════════════════─────────────────────────────────────── ┌──────────────────────┐ │ CW: re: mathematics │ └──────────────────────┘ @user-211 I agree! The problem is the limit as x->0 from the left and right trend toward different infinities, meaning it's neither -infinity nor +infinity. Which makes me think that it's the value that's exactly in the middle, AKA zero. Why wouldn't 1/0 be zero? Division is just inverse-multiplication, and multiplying anything by zero is zero. Why wouldn't division use the same rules? I don't understaaaaaand T.T ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧═════════════════════════════════════──────────────────────────────────────┘ === SIMILARITY RANKED === --- #1 fediverse/3326 --- ═══════════════════════════════════════════════════════──────────────────────────── @user-246 It's interesting to me that we can divide by infinity, but not zero. I feel like it's true that dividing by zero would equal infinity (or maybe zero too lol) but I don't know how to prove it T.T ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧════════════════════════════════════════════════───────────────────────────┘ --- #2 fediverse/3324 --- ═══════════════════════════════════════════════════════──────────────────────────── @user-246 If I follow correctly, the reason it's not is because you're dividing zero by two? meaning the magnitude of infinity would be zero. ... chat, is infinity just... zero, viewed from a different perspective? ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧════════════════════════════════════════════════───────────────────────────┘ --- #3 fediverse/3325 --- ═══════════════════════════════════════════════════════──────────────────────────── @user-246 so... if infinity is the inverse of zero, then when inverted would infinity also be zero? if so, it follows that the [spectrum/dimension/cardinality/direction] that the inversion is occurring upon might also have other steps inbetween. Unless it's a binary thing, like "top and bottom" or "present and absent". I wonder what those steps might look like? Clearly, since infinity minus infinity does not equal zero, the steps inbetween (if they exist) would not be numbers. If they were, then one single step from inverting infinity would be 1, but I don't believe that would be true. On the topic of rings, the axioms would be things like "a ring is a ring if you can trace a continuous line with a length of infinity across it's ring-like-surface"? I wonder what the inverse of a length is... Or perhaps you cannot invert a length, as to do so would give you a length of zero (in this particular ring-like-case) ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧════════════════════════════════════════════════───────────────────────────┘ --- #4 fediverse/4084 --- ═══════════════════════════════════════════════════════════──────────────────────── ┌──────────────────────┐ │ CW: re: -mentioned │ └──────────────────────┘ @user-1074 the more you try, the more you have to calculate, which is a problem, because endlessly recursive calculations create infinite loops, which frankly are impossible to compute because they defy computation! Not good, not ideal, no thank you, not for me, no thanks, not what I'd like. ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧════════════════════════════════════════════════════───────────────────────┘ --- #5 fediverse/46 --- ═════════════════════════════════════────────────────────────────────────────────── @user-36 neat thanks when I said 1-1 = 1/10 I meant 1/1 in decimal except the denominator is in base 1 meaning it's represented as 10 (since 10 in base 1 equals 1 in base 10. Or pretty much any other base.) I'm trying to figure out why 00 is undefined. There's a lot of math notation in that wikipedia article and I'm working through it bit by bit... I feel like there's a bug in the code of the universe and I'm trying to understand it. Like... why is dividing by zero undefined? That seems like a bug to me. ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧══════════════════════════════─────────────────────────────────────────────┘ --- #6 fediverse/44 --- ═════════════════════════════════════────────────────────────────────────────────── @user-36 So, you're saying the tally system doesn't make sense, and instead what I suggested for base zero is instead base 1? ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧══════════════════════════════─────────────────────────────────────────────┘ --- #7 fediverse/41 --- ═════════════════════════════════════────────────────────────────────────────────── @user-36 As a thought experiment, what do you think happens using this system to divide by 1? What about dividing by 0? Curious to see what you think ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧══════════════════════════════─────────────────────────────────────────────┘ --- #8 fediverse/42 --- ═════════════════════════════════════────────────────────────────────────────────── @user-36 I always conceptualized bases as "the amount of numbers you can stuff into a bucket before you spill over to the next bucket". Call it a holdover from learning binary a bit younger than most people would consider normal... Anyway with base 2 it makes sense. Put one thing in the bucket, and if there's something there then it spills over. But if the bucket is ALWAYS full, as in base 1, then you'd have to do a tally system like you said: essentially counting from 0, then adding one to the end making 10, then 110 for two, and 1110 for three, and 11110 for four, etcetera. The reason you leave 0 at the end is because zero is a number and must still be represented as a tally - it just uses a different symbol for our human interpretation. Zeroes deserve respect in base 1 just the same as any other number! zero rights are human rights... no that doesn't quite work, zero rights are number rights? nevermind that joke is stupid (continued) ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧══════════════════════════════─────────────────────────────────────────────┘ --- #9 fediverse/227 --- ═══════════════════════════════════════════──────────────────────────────────────── ┌─────────────────────────────────────┐ │ CW: mathematics-and-socio-economics │ └─────────────────────────────────────┘ humans are notoriously bad at large scales. tack a couple zero's onto the end and it increases in value to them as much as if you had given them two. 10+1010. but hey it's all 10's right? I think we severely overestimate the number of bad people in the world. I'm basing that on nothing but my feelings. I think people generally are just doing the best they can. that's what happens when you're oppressed in a livable way. in a time of peace you can be merry, but these days it's always been war. what can you do if your government disagrees with you? hey, what's the 10th root of 10? 0.1? dang that's so close to zero. I wonder if there's a calculation we can make that would end on a zero, but be unable to return? is that what dividing by zero is? just... casting it into the void? sure would make a lot of calculations easier if we could just return NULL ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧════════════════════════════════════───────────────────────────────────────┘ --- #10 fediverse/302 --- ════════════════════════════════════════════─────────────────────────────────────── ┌──────────────────────┐ │ CW: re: mathematics │ └──────────────────────┘ @user-211 math such as SUM(as x approaches infinity)(i*x) this would add i, 2i, 3i, 4i, 5i, 6i, etc off into infinity. would that give you complex infinity? a direction orthogonal to the X axis, yet infinitely far in the direction of y. it'd probably have a positive and negative side too, just saying. ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧═════════════════════════════════════──────────────────────────────────────┘ --- #11 fediverse/2357 --- ══════════════════════════════════════════════════════───────────────────────────── @user-1245 I disagree. What if we did not learn to count numerically, but instead viewed all values as percentages between 0 and 1? Essentially, as a magnitude between empty and full. That would radically redefine our mathematics, and it's just one simple change, one tweak, and suddenly negative numbers are just out of reach. ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧═══════════════════════════════════════════════────────────────────────────┘ --- #12 fediverse/37 --- ═════════════════════════════════════────────────────────────────────────────────── This would normally just be a weird way to divide except it allows you to divide by zero, which is kinda cool. ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧══════════════════════════════─────────────────────────────────────────────┘ --- #13 fediverse/45 --- ═════════════════════════════════════────────────────────────────────────────────── @user-36 Question - how do you do those cool superscript and subscript notations? Also: I don't think base 1 falls apart with negative exponents, for example consider 1^-1 ----- it would evaluate to 1/10 in this system, which is not 1/1. Another example, 1^-3 would evaluate to 1/1110, which seems accurate to me. As for 0^0, I guess I think it does equal 1? Bear with me: for any number n raised to an exponent e, you can write it like this: 1 * n * n * n ... with as many "* n"s as you have n's. for example: 1 * 3 * 3 * 3 = 9 or 1 * 5 * 5 * 5 * 5 * 5 = 625 in each case there's 3 or 5 instances of "* n" tacked onto the end. I don't know the math notation for that. now, when you raise something to the power of zero, it looks like this: 1 because there's zero "* n"s added to the end. For negative exponents of course you divide instead of multiply, which is why it ends up looking like a fraction. So, it makes sense to me that 0 ^ 0 would equal 1, because it'd look like this: 1 while 0^1 would be 1 * 0 ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧══════════════════════════════─────────────────────────────────────────────┘ --- #14 notes/division-by-zero --- ══════════════════════════════════════───────────────────────────────────────────── --{{{ introduction When division is explained at the elementary arithmetic level, it is often considered as splitting a set of objects into equal parts. As an example, consider having ten cookies, and these cookies are to be distributed equally to five people at a table. Each person would receive 10 / 5 = 2 cookies. Similarly, if there are ten cookies, and only one person at the table, that person would receive 10 / 1 = 10 cookies. So, for dividing by zero, what is the number of cookies that each person receives when 10 cookies are evenly distributed among 0 people at a table? Certain words can be pinpointed in the question to highlight the problem. The problem with this question is the "when". There is no way to distribute 10 cookies to nobody. Therefore, 10 / 0 —at least in elementary arithmetic—is said to be either meaningless or undefined. - wikipedia, division by zero, 7-12-23 alright I have several problems with this. I like the idea of dividing cookies, but I disagree with their conclusions. So dividing by integers works as they say, but division by zero is a little different - they say "the problem with this question is 'when'" when in reality 'when' is the same for this question as it is for any of the others. Obviously, zero is just a number. Why would this be any different? The computational actions necessary to complete this statement all occur at the same time, because they are by definition immutable. You cannot change any equation, you only generate new ones. Okay so here's my thinking. To answer the question "what is the number of cookies that each person receives when 10 cookies are evenly distributed among 0 people at a table?" we simply have to answer the question. "How many cookies do I get?" well, none, because you weren't at the table. In fact nobody was at the table, so the result is that nobody got zero cookies. You might even say you have a remainder of 10 cookies, as none of them were distributed. 10 / 0 = 0 remainder 10 ^^^ that's how I think it should be. I have an algorithmic justification, and excuse me as I don't have a mathematical proof or anything. Math was never my strong suit, there's too many symbols and strange names for obvious operations that get in the way of the abstract big picture. ahem... abstract: Given: x = 13 / 3 what is x? step 1: convert 13 to base 3 step 2: digit shift right by 1 step 3: convert back to binary --}}} --{{{ step 1: v start with the binary number 1101 which is 13 in decimal. To convert to a base 3 number, \___________________. \ | first start with the Least Significant Bit (LSB) which is 1. So our base-3 number starts with 0001. v Next, move to the next bit: 1101 ^-----It's a zero so we can skip it. Which means our base 3 number remains unchanged as "0001" v Next, move to the third bit: 1101 ^-----It's a 1, which evaluates to 4 in decimal, meaning we should add 4 to our base 3 number base 3 4 in base 3 is "11", which means we 0001 <----- 1 in decimal should have a base 3 number of "12" now. +0011 <----- 4 in decimal =0012 <----- 5 in decimal \_________ 2? -> yes, base 3 remember? Next, move to the fourth and final bit: 1101 ^ --it's a 1, which evaluates to 8 in 0012-----.____________ decimal. 8 in decimal is "22" in +0022-----. \ base 3, which means we need to =0111 \ T---- add "22" and "12" in base 3 \__________/ to get our final number of 13. Which should evaluate step 2: to 0111 in base 3. .____. bit shift |0111| to the right, |>>>>| |0011|--->1 underflow .----. meaning the base 3 number is now 0011 with an underflow (remainder) of 1 step 3: convert back to binary, meaning 0011 in base-3 becomes 4 in decimal or 0100 in binary. Store the underflow as the remainder. =============================================================================== = okay that's great and all, but what does this have to do with dividing by zero? great question, me. I have two questions I want to pose to you: 1. what happens when trying to divide by 1 with this algorithm? - you convert to base 1 \ wait hang on base 1? Sounds made up... Well, its not! or at least if it is, then I'm the one who made it up so... yeah | okayyy how does base 1 work? \ glad you asked. --}}} --{{{ bases --}}} --{{{ decimal (base 10) --}}} --{{{ binary (base 2) --}}} --{{{ digit shifting --}}} --{{{ bases higher than 2 and not 10 --}}} --{{{ base 1? base 0? --}}} ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧═══════════════════════════════────────────────────────────────────────────┘ --- #15 fediverse/276 --- ════════════════════════════════════════════─────────────────────────────────────── ┌──────────────────────┐ │ CW: mathematics │ └──────────────────────┘ why the heck would -11/2 be defined but 1/0 not be? seems kinda sus to me. maybe it's just... not reducible, the same way that 5+i isn't? ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧═════════════════════════════════════──────────────────────────────────────┘ --- #16 fediverse/3030 --- ═══════════════════════════════════════════════════════──────────────────────────── @user-570 ooooo separating additive and multiplicative, I love that. I do like specificity unless "increased" and "more" always corresponds to +10% and +50%, or if the "rate of increase" is a stat stored on the character then "increased" could increase quality by however-many percentage,, while "more" could be "more soldiers" x(charisma_stat) I tend to think of percentages like "0-100 (or more) stacks" of a particular effect, so I think that's just how my brain works... xD clumping them up into discrete groups - like, anti-abstracting, or measuring things that are just a few. "is this belt better than this one?" "is this pair of tongs even for larger buffs like +10% or +50% or whatever, those are just... 10 stacks, or if percentages are usually round numbers like +10% and +50% then like... +1 stack which calculates to +10% the hard limit vs math limit thing you said is amazing ^_^ ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧════════════════════════════════════════════════───────────────────────────┘ --- #17 fediverse/3322 --- ╔═══════════════════════════════════════════════════════───────────────────────────┐ ║ @user-246 │ ║ │ ║ yes, when defining with numbers it's easy because one is one and that's done. │ ║ │ ║ with concepts such as infinity or direction or cardinality, it's more │ ║ difficult because you need more than just a "magnitude from zero" to describe │ ║ them. Rules means more contradictions, which is totally okay! It just means │ ║ you need more than one definition of "infinity" for example, for different │ ║ contexts. │ ║ │ ║ use a scalpel for surgery or art, when precision is needed, use a pocket-knife │ ║ like a leather~~man~~daddy for tougher tasks like whittling a spear or │ ║ throwing a spear or stabbing fascists with spears - where was I going with │ ║ this? oh yes: │ ║ │ ║ when thinking of sets, to me infinity is more like... "too many numbers" like, │ ║ the meme with the guy who is having difficulty holding too many limes. They │ ║ overflow and spill out of your set-like-container, no matter how you define │ ║ the boundaries of the set. "does the set of all sets include itself or does it │ ║ overflow" kinda vibe. │ ║ │ ║ the idea of a chesspiece disagreeing with math lol! │ ╟─────────┐ ┌───────────┤ ║ similar │ chronological │ different │ ╚═════════╧════════════════════════════════════════════────────────────┴──────────┘ --- #18 messages/141 --- ═════════════════════════════════════════════────────────────────────────────────── Why would we say not to divide by zero? We literally do it every time we use the percent sign smh [silly] ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧══════════════════════════════════════─────────────────────────────────────┘ --- #19 fediverse/1625 --- ════════════════════════════════════════════════════─────────────────────────────── ┌──────────────────────┐ │ CW: mathematics │ └──────────────────────┘ EDIT: Ooops, sorry, should have content warning'd this post two incredibly useful tools I found for boolean logic in mathematics: | f(x) | / | f(x) | or more visually: | f(x) | --------- | f(x) | this will return a 1 if f(x) evaluates to a non-zero value, and 0 if f(x) evaluates to zero. Pretend there's an infinitesimal at the bottom if you're one of those weirdos who think dividing by zero doesn't equal zero... the other tool is this: ( A * B ) + ( (1 - A) * C ) or more visually: ( (0 + A) * B) + (1 - A) * C) This will evaluate to B if A is 1, and C if A is 0, essentially creating an "if true" check. Note that it doesn't work if A is neither zero nor one, but that's what the first tool's for. ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧═════════════════════════════════════════════──────────────────────────────┘ --- #20 fediverse/1715 --- ════════════════════════════════════════════════════─────────────────────────────── @user-246 true, but what is a poem if not a silly construction of phrases? Those words don't belong together, what are you doing! And yet it fills you will a feeling that the author intended, thus being poetry as a joke. problem is if everyone says the same joke, it gets kinda... old... hence why you should express yourself as much as you can. I wonder if fewer people are "alternative" these days because they all started hanging out on the internet and trying to differentiate themselves amongst each other instead of amongst "normal people"? Weird thought, srry haha ┌─────────┐ ┌───────────┐ │ similar │ chronological │ different │ ╘═════════╧╧═════════════════════════════════════════════──────────────────────────────┘ |