this post was submitted on 11 Sep 2025
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Not a number
I said something like "any number, including infinity" in some exam at uni. Got an angry red text saying "not a number" next to it.
Just put ℵ₀ as it's probably what you were intending anyways (Aleph 0 is a number that basically represent all of the countable numbers [1,2,3,4...] put together, the "smallest infinite number")
Using a concept from one course in one that didn't teach/refer to the concept before is a good reason to get an answer rejected.
Note that א_0 is used in set theory and adjacent topics, while infinity as a value (or object) comes from function analysis, the two have different definitions and mean different things and are used for different purposes.
why is that automatically a reason to have it rejected?
because modern academics don’t always actually care about teaching people and are often more concerned with weird ego competitions.
people might try to justify this sort of behavior to you but just know drawing the dots between the constellations in human knowledge is what you’re supposed to be doing, even if you don’t do it well.
i'm so fucking sick of school apparently just being a place to memorize things for a test and then flushing that "knowledge" in favour of the next round of data..
If you're tested on using a tool (a course's subjects) you're expected to use the tool.
You're tested on a drill, of course you're not supposed to use a wrench, even if it does the job, success on the course test is (or at least supposed to be) a proof of you knowing the subject matter, this includes knowing the tools that are given to you.
i understand the architecture and ethos of modern academia/pedagogy, i don’t need an explanation.
i’m just not convinced that this methodology or this culture is the best way to instill skills and knowledge in individuals.
it certainly makes people good at becoming corporate peons later in life, only learning to problem solve in limited contexts where a higher authority grants you permission on what to think or use in your solution building process.
i’d like to live my life in a way that doesn’t make nearly religious appeals to a higher power, however. i’ve met many peers who will teach their students exactly contrary to the traditionalist take you’ve shown here… and you know what? their students seem to, anecdotally, have better outcomes than the stuffier traditional ones. the traditional model assumes that, like you said, showing didactic ability to repeat the exact steps and methods taught in the course demonstrates proof of conceptual knowledge in the subject. modern research into how human learning actually works has demonstrated handily that this assumption is entirely unfounded, and that those two things don’t directly correlate the way many would imply. the traditional educational model is broken and no longer serves modern society in any real way other than as a class barrier. you can learn basically anything you want nowadays on the internet. society won’t play ball with you until you fork up an arm and a leg to go “network” at a college, usually, though…
You need to take a few steps back, you're making a very long reply to something i haven't said.
I'll be clear, i DONT like regurgitating proofs in a test, it's literally where i am most likely to lose points.
I WAS talking about solving a test question using material from another course, which is silly because that would be admitting "i can't use the tool i was supposed to practice with during homework".
Because as a problem solver, you're expected to be able to have a variety of tools to solve problems with, and you should want that, to make sure you solve problems using tools that make the solutions better in one way or the other.
On the contrary, if i allow solving a test using a different course's material then what the fuck is the test measuring? It certainly can't be used to say "this person knows how to use what i taught them".
I mean, if you don't want to read people's replies then don't participate in discourse on an online forum. Idk what to tell you there. Not every single point in a thread pertains to you personally, and my response was relevant to the discussion at hand.
Well, this isn't the point of tests, which if you considered my earlier replies, was actually my entire thesis, for the most part. But for the sake of debate, lets concede this point as just being true and see what happens. Assuming that a test is intended to show a mastery of the course's tools, using a tool from 'outside' of the course doesn't necessarily demonstrate that you "can't use the tool you were supposed to practice with." You either used the 'required' method correctly, demonstrating tool competence, or you didn't. If the problem gets solved by a different route, that's not necessarily a binary condemnation one way or the other. It's just more data.
Further, if we grant that this is the point of a test in education... then if it can be solved by an external tool or method, how is that the fault of the student? The student anticipates the instructor to design the course and test in a manner that might require the intended solutions... if it can be easily solved by alternative means, that is a failure of the test design, not the students. Rejecting these answers categorically is punishing students for the teacher's failures.
Finally, even in your own analogy, your logic doesn't really hold up as a conclusion. A person who uses a wrench to complete a drilling task has still demonstrated both the ability to get the job done and problem-solving flexibility. If the examiner wants to know "can they use a drill," the question must force the use of a drill. If it doesn't, the metric itself has failed. Essentially, you are saying that a test's whole purpose is to measure the student's ability to use a proscribed tool. Yet, we are still sitting here arguing about what happens when a test... doesn't fulfill that purpose? Do you not see the clear contradiction starting to appear here? This isn't just a case of bad test design, the counterexamples here can't just be easily squared away with a No True Scotsman argument. This definition of what makes a test 'useful' is just logically incoherent...
In reality, tests don't measure the student's ability to use tools. The purpose of a test is decided by who designs the test. Often, however, the goal is to best glean student's cumulative knowledge. We've famously known for hundreds of years, however, that you can't directly know anything outside of your own existence. So, in practice, tests measure a many different things. Your zealous and iconoclastic views on academia basically preclude the possibility for cross-disciplinary practices and knowledge. All of human knowledge is people smearing the lines we draw in the sand. Sometimes we see a prettier picture than before.
You're overcomplicating your reply and it doesn't make it look any smarter.
You cant force a solution in a math question from the question, and also have the question not be trivial, do you actually have any experience in using higher level maths or are you speaking out of your ass like the guy i was replying to originally
That's not generally true. That's entirely dependent on the question and whoever designed it. Solve for x in Ax = b can be solved a metric fuckton of ways. Solve for x in Ax = b using Gaussian elimination is solvable in much fewer, often one, way. That's just a trivial example but the idea that you can't both force a solution and have a non-trivial question is demonstrably false to anyone with experience.
Ah, so now length is the crime and experience is the verdict? Fascinating. Meanwhile, the logical contradiction in your own position remains completely untouched. I have a master's degree in ML/AI so I actually have quite a lot of experience in mathematics.
Do you actually have any experience in working in academics, or are you just 'speaking out of your ass'? It's not particularly relevant, either way. Your position would be more in-place at a high-school geometry class than in a genuine collegiate setting, let alone in academia or industry research.
It has a good reason, i explained to the guy below you and don't want to copy paste
It transcends numbers. Infinity is their God.
Infinitely more
Well... Infinite is not a part of the set of real numbers but infinite is part of other sets of numbers, like hyperreal numbers. So, technically, it is (sort of) a number. I guess it would be a class of numbers, but it isn't not a number.
Unless you're a computer engineer, in which case, Number.Infinity is my final answer.
I could define a special class of numbers that includes my cat, and it wouldn't make my cat a number either.
If you can't do arithmetic with it, it's a not a number.
You can do arithmetic with infinite. Defining an operator on the set of hyperreal numbers is pretty simple. It's actually really cool, because it'll teach you about scales of infinities and infinitesimals.
And, while you could define a set to includes your cat, that doesn't make your cat a number. I can make a set of six apples, and none of those are numbers. That is categorically not how numbers work.
I mean, you can square root a negative in complex numbers, but you can't in real numbers. That doesn't mean that the square root of negative one isn't a number.
The "problem" is defining what you mean by "infinite" specifically. Infinite is an adjective that you can assign to a set of numbers, and the "infinity" would be the summation of that set, but what set are we talking about? Is it all natural numbers? Rational numbers? Real numbers? Even numbers? Powers of 10? These are all different infinities with different properties. Some can give very odd results, especially with analytic continuation. The set of natural numbers {1,2,3,...} can be evaluated to infinity (ℵ₀) or -1/12. You have to get more specific when dealing with infinite numbers; you need to define what infinity is when you work with it.
Incorrect. example: א_0 is an infinity, specifically a size of the natural number set, and is not a sum of any set. Another example: infinity in real function analysis, is a concept of unbounded growth, either positive or negative.
Incorrect based on previous mistake. You're describing a series sum, no series sum is 0_א, that's a major mistake, as it is specifically a set size and not a natural number.
And the 2nd concept you're referring to leads to a contradiction as a sum of positives must be positive, this means that in order to get -1/12 you must make a mistake.
These are all already well defined (except for (naive) set theory, but it's irrelevant to this), and you don't need to "define what infinity means when you use it", that's nonsense.
You are literally proving my point. You have used at least three different definitions when using the word "infinity". THAT is what I mean when I say you need to define what is being referred to by "infinity". It is not a single concept in mathematics.
To address your specific points:
ℵ₀ is the cardinality of countable infinities like natural numbers, rational numbers, etc.
If you attempt to find the summation of an infinite series, you approach infinity.
I never claimed that ℵ₀ is the summation of a set. You base so much of your commenr on a claim I never made.
I said that the natural numbers can be EVALUATED to either infinity or -1/12 and I made sure to define what I meant by infinity to be ℵ₀. If you think that it is incorrect that the natural numbers can be evaluated to -1/12, you have no place trying to correct others on mathematics. Just watch this eleven year old video by Numberphile for proof.
Your fundamental misunderstanding and flip-floppong between definitions of infinity male my point glaringly clear here.
Don't be a dumbass and cite a fucking YouTube video to someone giving you definitions, i honestly guessed you were going to come with VSauce and Numberphile even before you made this reply because i watched them so many years ago.
I've studied these at uni, I've even cited the courses I've studied these from. So don't go "your fundamental misunderstanding blah blah" bro you're citing a YouTube video.
Me citing a youtube video proved your statement wrong and this is your response.
Guessing you failed the class you were studying this in? Definitely doesn't sound like you remember much.
You're only raging because the only defense you have is a YouTube video, which i already saw the proof of about 10 years ago.
At least give an actual insult instead of impotent "i guess you failed the course you don't remember blah blah", for a course I finished the second part of last semester. So no reason to forget it as I'm expected to use it still.
You should have read about the topic instead of whatever this response is.
You are the one devolving to ad hominem. You haven't addressed a point I have made in your last two comments. You seem to think that a YouTube video is some lowly source that doesn't warrant merit. How sad then that you were proven wrong by a youtube video. YOU are the one who lacks any defense because you KNOW you were wrong, and by failing to address my points with facts you are proving that point.
"how sad" sure I'm at uni and you need a YouTube video to defend yourself because you don't know the subject matter, andyou are trying to get my attention.
You have more important stuff to do than continuing this thread, might i suggest reading about the subject matter on Wikipedia?
Lmao you replied to me in the first place, exactly how am I trying to get your attention? I already had it from the beginning...
You gripe about the merits of a youtube video (which I only linked to because I'm not gonna spell the whole damn proof out for you here), and you tell me to go read wikipedia? I'm guessing you are just being sarcastic there, because if not... sheesh. Yikes. Oof, even.
Wikipedia is extremely good for mathematics, that's one, two is that the "proof" is inherently flawed as it leads to a very trivial contradiction.
I could walk you through the proof to so you how it's wrong, but you are obviously more concerned with proving to a university student that your high school level understanding of maths is better because you saw a YouTube video.
You should reflect on that.
I stumbled upon your other dialogue here while browsing the thread. I'm honestly not certain whether or not you're just trolling, but in case you're being serious... a word of genuine advice from someone who has gone into a field that has a lot to do with mathematics:
You seem like you're an undergrad student, potentially from the UK, potentially majoring in mathematics or a mathematics adjacent field. You do seem passionate about it, I can give you that. But seriously, friend, the way you handle discourse, debate & dialectic, and reasoning are all massively ill-equipped to actually handle working in this field. If you don't change you will fail in your career. This isn't meant to be mean, it is a legitimate and fair warning. I've met a lot of people just like you over the course of my own career, and they don't last very long if at all.
Separate ego from argumentation. Engage evidence on its own terms. Recognize that complex results sometimes defy intuition. Value clarity and logic over signalling status. The responses you are getting here are really light compared to what actual supervisors and peers are going to throw at you out there. You utterly failed to sway or convince anyone because you refused to even try. The problem is patently you here. I suppose I'm trying to tell you here and now, when it's just an irrelevant internet forum, versus later when your dreams and economic security get crushed because you can't maintain a research position. If you just continue on how you are, you're going to alienate all your peers. Nobody wants to work with someone who's more concerned with personally being right than finding the truth. That's what you've done here, in all the comments of yours I have read. For example, if you were actually concerned with the truth you would've outlined your reasoning for why the proof regarding the limit of -1/12 is incorrect. You didn't even begin outlining or clarifying the problem space. What is it that you find objectionable here? Because I don't necessarily disagree with you, that limit does imply nonsensical results in a broad context. That's not the context it is posited in, however. -1/12 is pretty famously derived from the Riemann Zeta Function evaluated at -1. If you'd engaged with the other guy's source in good faith, you'd understand that he was approaching the problem in that space. You'd then be able to formulate a counterthesis that appropriately addresses the argument at hand instead of strawmanning and posturing. You didn't do that though. Why? Because you were more concerned with being personally correct than finding out the truth. So your discourse stalled and you convinced nobody of anything at all! We're not here to debate, we're here to engage in dialectic.
Final word of advice - drop the ad hominem attacks, glaring assumptions, and refusal to engage with sources based on tenuous reasons. Those are going to prevent you from breaking into the career in the first place. Don't attack people, attack arguments and lines of reasoning. Attacking someone personally doesn't do anything but undermine your own credit.
Hahaha ok then show me how the proof is flawed? You will have a LOT of mathematicians and scientists extremely interested in your proof.
Also, I learned this stuff in high school, but I went to college a decade ago so... maybe when you get done with math 253 and get into some higher level courses that cover complex analysis, you will change your tune.
Wikipedia IS indeed great for mathematics, as is a youtube video from university professors who teach and apply these mathematics. Exactly what is wrong with a youtube video featuring high level math professors teaching concepts about mathematics? You just keep saying "durr your only defense is a youtube video" when it literally is not "my only defense" it is just a single source I used to prove you wrong. You never gave a rebuttal to my point, just tried to attack the source. You say you know about the video and the concept, but you still make false and baseless claims that I already proved wrong. You are simply butthurt that you were wrong.
This guy argued with me somewhere else in this thread. He engaged in all the exact same rhetorical strategies and was similarly bone-headed when it came to actual, applied concepts in math. I don't think you're gonna get very far with this one, man. BRAT is an acronym for BlackRoseAmongThorns, and they're really living up to the name!
...? I believe I said the set of hyperreal numbers, which would contain the real numbers cross joined with the set of infinites and infinitesimals. Technically, the infinity that bounds the natural numbers would be any of those infinites. I can't really point to one specific infinity.
Infinity wouldn't be in the set of natural, rational, real, or even complex numbers. It acts as a boundary for all of those sets of numbers, but you could have a set that also includes infinity, in addition to those sets, making them the extended number set.
However, I want to point out an issue with what you said about those being different infinities... That isn't strictly true. Natural numbers, rational numbers, and powers of ten are the same level of infinite. Crazy as it is to imagine, the sets can be functionally mapped to each other. They have the same infinite of elements to them. It isn't until you add in those irrational numbers that the level of infinite increases. There is a higher order of infinite more numbers in the irrational numbers than in the rational numbers, so that infinite IS bigger.
ℵ₀, the infinity that represents the cardinality of natural numbers, would not be "any infinity" in the set of hyperreal numbers. You have a fundamental misunderstanding of the concept of infinitea if you cannot point to a specific number that "bounds the natural numbers" because that number is ℵ₀ and can be pointed to. It is the only countable infinity. Bring in irrationals and now it is uncountable, because there are an infinite number of numbers between 1 and 2. You can never reach 2 if you counted every number between 1 and 2. The cardinality of irrational numbers is ℵ1, a distinctly different and larger infinity than ℵ₀.
Sets like naturals and rationals may have the same cardinality, but they are not functionally the same. Cardinality is just one attribute they share. The powers of 10 cannot be analytically continued to -1/12 like the natural numbers can. Therefore they are functionally different.
Yes, obviously there are different ordinalities to infinites, but for the express purpose of this comic, the particular infinity does not functionally change the comic. The infinity that bounds the real numbers is technically the one that matters, which you are suggesting is somehow different depending on the collection of numbers used to calculate it, which it doesn't. The collection of powers of tens is the exact same as the collection of natural numbers, at infinite scale. It is not some power more, or different. The Euler zeta function doesn't work like that.
Also, there are also an infinite amount of rational numbers between any two rational numbers, even without irrational numbers. The ordinality of the infinite doesn't matter about that, but the ordinality of irrational numbers between them is bigger.
https://en.wikipedia.org/wiki/Arithmetic
Sure you could probably apply these things to "operators on the set", but that's completely missing the point and pretending that something you've applied to infinity to get a number, is the same thing as infinity itself. Turning infinity into to a number by treating it in some other context, is not the same thing as infinity being a number.
It's like trying to claim that 1 is an even number because look, all you need to do is define a set of rules that multiplies it by 2.
That was exactly my point. It's not how infinity works either.
Okay. All of those operations exist on the hyperreal numbers, or even just the extended real numbers, so I don't see the issue. It's not turned into a number, it IS a number, and it doesn't represent anything other than itself in those contexts.
Hey, you know what, I'll make this easier for you. Name a mathematical operator you can't do on infinity.
You can add it, you can subtract it, you can multiply and divide it, square root it, exponent it. You'll get some weird answers for some of those, like subtracting infinity from itself, but it's still doable. I mean, unless you're suggesting zero or negative one isn't a number.
If you can’t do something in any meaningful or consistent way, you can’t do it.
You “can” add 1 to infinity, but it doesn’t give a result that is measurably 1 greater, and therefore has not obeyed the basic axioms of arithmetic.
There is no number you can add, subtract, multiply or divide infinity with, that results in zero. Unless, as I keep saying, you’re acting in some meta-contextual space in which infinity is counted as a countable “representation” of infinity, which isn’t the same thing as infinity being a number. I realize this is exactly what you are trying to do, and it’s not as clever as you seem to think it is, so you can stop repeating yourself.
Infinity plus any number besides negative infinity in the extended number line is always infinity. That seems pretty axiomatic, buddy. Infinity times a positive is infinity. Infinity times a negative is negative infinity. Are you suggesting that all numbers follow all rules of each other? That would be silly. There are always exceptions. Zero to the zeroth power, for example. Infinity is related to zero in a lot of ways.
As for your saying that there are no ways to apply infinity to equal zero, that's also not strictly true. We can absolutely converge certain infinitely scaling functions to 0, even in real numbers or integers. You can even subtract infinities to get 0.
Infinity does not always represent a concept. It only represents a concept in real numbers because it's not a real number. But neither is the square root of negative one. Unless you would like to show me 2_i_ of something. But 2_i_ is undoubtably a number.
It's not clever, you're just wrong. I feel like you can't accept that.
Also, one divided by infinity is zero in an extended number line.
See, again with the added qualifications and sleight-of-hand redefinitions. It isn't equal to zero, it's just zero "in an extended number line". You're being argumentative and contrarian for its own sake, and I think you're probably intelligent enough to know full well that that's what you're doing, but not quite intelligent enough to realize that you shouldn't.
Also,
Can you knock off the obnoxiously condescending phrases every other sentence? They don't add to your argument, they just make you sound like a prick.
Infinity isn't a real number, pal. So, I have to qualify it, because you'll say that it's impossible to divide by zero, chief. Unless you have an answer that isn't infinity, friend. I can remove the qualifier if you'd like, and the answer is still technically correct, boss. I am willing to accept I'm wrong if you can answer which number one divided by zero is, I could very well be wrong.
Apologies for my upbeat tone, I'm Canadian, you see, and I believe that we should always use a friendly tone when teaching people new things, ya scamp. I realize this probably comes across to you as arrogant, but I think that might be more related to you thinking I'm wrong when I'm not.
For reference, saying "in an extended number line" is the equivalent of saying "including infinity".
Like, if it's the real number line, extended real number line means real numbers and infinity and negative infinity.
She is to me.