The Japanese word is Rei. You should take note that the common numbering system in Japan consists of Chinese numbers (rather than Japanese ones used for counters and such) and Arabic numerals.

I can tell you that possibly Europe never conceived the idea of zero until Arabic numerals arrived in Europe. Prior to that "zero" was less a number than a conceptual signifier for "nothing." The decimal and placeholder form of zero cemented it as an actual mathematical number rather than a concept.

For example, "infinity" is a concept rather than a number. It also holds little mathematical value because you can not apply arithmetic to it. Another example would be NaN. Imaginary numbers are often times grouped in the concept of NaN until they are signified by i so you can apply arithmetic to them.

In the same way the Arabic number 0 replaced the conceptual "Roman numeral" N.

>>9132777 It doesn't hold mathematical value. It is a mathematical concept.

You can perform basic arithmetic on numbers with numerical value. There is a small niche in which you can play with the value of infinity, but given that it is not a real number, it lacks value.

>>9132941 Infinity is not a definable value. You can not say the value of something is infinity.

If we were talking about the monetary value of something, you could say something is worth "$5" but you would not say something is worth "infinity dollars". Because infinity dollars isn't a number or a value, it represents the concept of "priceless". How long is a road? Not "infinity miles." Either the road is "endless" or it is "infinitely long" which is placing a conceptual qualifier on long. Like "Roman numeral" N, is represents a concept of "not having a value" or "not definable using value"

>2. With certain caveats, you can, in fact, perform arithmetic operations on infinity. This was already stated, there was no need to repeat it.

>1. Arithmetics is just a small subset of mathematics. Arithmetic is not a small subset of mathematics, but the basic core of which other sets of mathematics base themselves on. Arithmetic are some of the vital building blocks for more complex branches of mathematics, and most practical (as opposed to a few purely theoretical) mathematics have components that can be reduced to arithmetic.

That is a formal construct must be built on the foundation of arithmetic in order to calculate things that do not fit within the arithmetic model, yet this new paradigm uses and is built upon arithmetic rather than being divorced from it. It is basic and fundamental rather than a "small subset" and makes up the vast majority of human calculations, especially when you consider the arithmetic operations in higher math.

And by mathematical value, it is obviously means in the context that infinity is not meaningless, and it is of value to mathematics, but within mathematics outside of some very specific models, infinity lacks a definable mathematical value. Trying to argue the first is just reading into it what you want to read.

>>9133114 I am a math major. Firstly, there are different infinite sets. And I have to say I spend most of my time struggling with problems involving sequences, function series, nets, sets whose cardinality is bigger than aleph null.

In fact, by generalizing properties to infinite sets, coupled with Zorn's lemma, modern mathematics becomes incredibly powerful. David Hilbert saw the genius in George Cantor when Cantor stopped treating all infinite sets as one and the same.

Arithmetic is a big part of elementary mathematics. But it's called elementary for a reason. You don't go to college to learn how to do additions faster. Modern mathematics, especially analysis, is concerned about things like infinite-dimensional holomorphy and other abstract entities where basic tools over finite sets are of little help. Just try proving every vector space has a basis, for instance.

Many properties that are obvious in finite-dimensional spaces (like every norm is equivalent in finite-dimensional Banach spaces) become very hideous and non-obvious, or even wrong, in infinite dimensions. So no, I personally care little about any real number or finite sets. But I care a lot about properties of infinite sets and structures.

>>9133256 Infinity sets are not numbers, and not values. They are mathematical objects, but not numbers, which isn't unusual, in lower levels of math there are lots of non-numerical objects. Sets contain numbers/values but are not numbers/values.

>Modern mathematics, especially analysis This is wrong, modern mathematics excludes things like meso-American and Roman numerical forms and their methods of arithmetic, however the bulk of mathematics today is elementary. Arguably every calculation done on a computer utilizes arithmetic on some level. Most calculations have arithmetic operations.

What you mean if the cutting edge where math specialists attempt to either develop new theory or at least be on the cusp of new theory (I say this because inevitably most math majors will end up doing applied math rather than developing new theory) rather that practicing established applied mathematics.

Now what you seem to be arguing is that "infinity" is of value (as in worth) to mathematics which was never denied, that interpretation is simply taking the word value out of context which is clearly not meant if you read the posts.

>>9133303 At least the Chinese invented unique numbers for base 10 instead of the stupid Roman Numeral system used until the 18th century in Yurop, even if they did miss out on placeholder 0s. Clearly sandpeople are the most advanced race.

>This is wrong, Stop being a sperglord and try getting a math degree in analysis. You are spouting ignorance, plain and simple.

>the cutting edge where math specialists attempt to either develop new theory or at least be on the cusp of new theory As opposed to the rest of mathematics where people put numbers into formulas? We have a word for that. It's called "bean counting", definitely a subset of mathematics.

Mathematics is first and foremost problem solving. You might have been taught how to use a calculator instead of mathematics, but that is not my problem.

>>9133342 >Stop being a sperglord and try getting a math degree in analysis. You are spouting ignorance, plain and simple. Math majors are by definition sperglords because you choose to ignore applied mathematics. You can not say that infinity is a number, and you can not say a set is a number, and you sperged because you felt infinity was being marginalized.

>Mathematics is first and foremost problem solving. Exactly. Most problems are solved using some basic arithmetic.

>We have a word for that. It's called "bean counting", definitely a subset of mathematics. One, analysis is also a subset of mathematics, and two, you should know that counting or enumeration is the most basic form of mathematics. Arithmetic a tier above counting.

>You might have been taught how to use a calculator instead of mathematics, but that is not my problem. You're just a fucking idiot because you think your complex number theory is somehow relevant in the problems faced by most people. Most people don't even have problems that can be solved by such advanced mathematics. Even in engineering, the problem solving profession, it mostly goes through basic arithmetic to calculus.

Now tell me you don't use a calculator.

>>

Cudder !MhMRSATORI!!FBeUS42x4uM Thu Jun 7 06:19:39 2012 No.9133371

It says a lot that Arabic numerals are one of the few things *everyone* has managed to standardise on.

Lesser known is the fact that it was originally a little-endian system as Arabic is RTL, but those adopting it didn't notice and unfortunately we're now stuck with the somewhat less logical big-endian ordering.

>>9133340 By definition it can not be a placeholder 0 because it does not use the same symbol in different decimal places. Secondly to say "22" as you would in a placeholder system would mean "ni-ni" rather than "ni-juu-ni." It could only be barely arguable that it is a placeholder if 22 is "ni-ni" but 20 is "ni-juu"

>>9133114 >You can not say the value of something is infinity.

Yes, you can.

>If we were talking about the monetary value

But we aren't.

>Arithmetic is not a small subset of mathematics, but the basic core of which other sets of mathematics base themselves on.

That's wrong. You've never formally studied math, it seems.

Logic and set theory are the basic core of mathematics. Arithmetic is just a small subset of math with particularly easy to understand and ubiquitous applications in everyday life of common people.

>most practical (as opposed to a few purely theoretical) mathematics have components that can be reduced to arithmetic.

And you're mistakenly assuming that those few select things you can apply math to are the only practical uses of it.

Of course those numbers are not exactly the same as the infinity you may know from mathematical analysis, but since it's already apparent you guys are mistaking a few select branches of math that you learned in (high?) school for math as a whole...

>>9133370 >Math majors are by definition sperglords because you choose to ignore applied mathematics. You can not say that infinity is a number, and you can not say a set is a number, and you sperged because you felt infinity was being marginalized. I'm not the person you're replying to, but mathematics is the study of mathematical systems. Applied mathematics is a different subject that concerns itself with finding correspondence between those systems and the real world. He's not ignoring mathematics; how mathematical systems are applied to the real world has no bearing on their properties as purely axiomatic systems.

>Exactly. Most problems are solved using some basic arithmetic. Some mathematical systems enable you to solve certain problems with basic arithmetic, but in the context of pure math, it's the logical properties of the system that are studied, not applications of those properties.

>One, analysis is also a subset of mathematics, and two, you should know that counting or enumeration is the most basic form of mathematics. Arithmetic a tier above counting. I believe that's essentially what he was saying in the part of his post you quoted.

>You're just a fucking idiot because you think your complex number theory is somehow relevant in the problems faced by most people. Most people don't even have problems that can be solved by such advanced mathematics. Even in engineering, the problem solving profession, it mostly goes through basic arithmetic to calculus. Again, the applications of mathematical systems are irrelevant to any discussion about the systems alone.

>>9133455 I hope you realize you wouldn't have that shiny toy you're typing this on that connects to the website that lets you publish what you type without all them math majors.

...though letting you do that arguably is detrimental to society, so I see your point.

>>9133370 You sound mad. Most people also believe in God and can't solve a quadratic equation (they don't even know what that means). Join them if you want.

You are the kind of kid that pisses himself when he learns about things like Fourier series in engineering. Applied mathematics uses a LOT of advanced theorems from pure mathematics. Do you know how a computer calculates sqrt(ln 2)? Maybe it throws a dice to calculate it? How cryptography works? Where quantum mechanics comes from? How transistors work? Ever heard of spectral theory (hint: David Hilbert and quantum mechanics)? How nuclear scientists model plasma flows? Well I guess it's all magic to you, people just make up stuff in maths for no reason and maths is just a way to torture students.

You are the kind of kid that thinks applied mathematics consists of just using a calculator. Then college tells you it's more than that. Then you don't know where the formulas come from. Then you try to memorize all the formulas. Then you piss yourself because you don't understand anything. Then you go post on 4chan how stupid engineering/science is because it's all memorization, formulas and no skill.

No mathematicians ignore applied mathematics. They ignore problems that are already solved in reality. They study new cool things, use logic to redefine the frontiers of knowledge and come up with formulas for the rest of scientists and physicists. While you sit there wondering where the hell Fourier series comes from and think mathematics is all about calculations and making stuff up that nobody uses.

>>9133509 Actually engineers can't solve anything without things handed to them by mathematicians.

When a new real-world problem pops up it's mathematicians who develop a systematical way to solve it, while engineers sit there being useless robots until the mathematicians update the AI for the robots.

Oh god. I never knew math majors were worse than philosophy majors. At least a philosophy major can be somewhat intriguing even if they put up the same bullshit.

>>9133533 >why don't you actually do anything useful? >Philosophy Major: Everything is based on philosophy, you wouldn't have some of the most basic things in your life without it, now consider the following theory that may change the way you see the entire world

>why don't you actually do anything useful? >Math Major: Everything is based on math theory, you wouldn't have some of the most basic things in your life without it, things like sequences, function series, nets, sets and plasma flow

>>9133543 >And neither is the infinity you know from real analysis. I can't believe how retarded you are. This is exactly why absolute infinity is a concept and not a number. It means without any limit, in the sense that you can not "move the goalposts." Every time you do so, absolute infinity is what lies beyond.

>>9133567 I don't think you proved anything except betting buttmad. I mean the whole thread is about 0's, and infinity was only used as an example of a mathematical concept. And if you were really a math major you would know that there exists an infinity that is a non-number concept.

Also the snobbery doesn't come from the correcting, it comes from the whole, we are better than you are you would all live hopeless stoneage lives without nuclear plasma flow without us spiel.

>>9133576 They use it in two different ways, they just haven't quite caught up with two different terms to differentiate between them. Too busy lauding themselves on imageboards and forusm.

>>9133564 First of all, you don't seem to realize what absolute infinity is. It's not an easy concept to comprehend, math as a whole struggles with it, so I don't blame you. The problem is, you don't even know all that, you're just treating is as some kind of buzzword you can bullshit with.

Second of all, the goalpost moving refers here to the logical fallacy you're committing. In this case, the trick of suddenly replacing infinity (all the various kinds that are actually defined and used in mathematics) with another, more specific concept. And it doesn't even help your case in any way, but it was just too cute not to point out.

>>9133590 >First of all, you don't seem to realize what absolute infinity is. It's not an easy concept to comprehend, math as a whole struggles with it, so I don't blame you.

>>9133572 Actually the math major guy is me, not the guy you're replying to.

And since you couldn't bother to read the thread, this is what I responded to : >It (infinity) also holds little mathematical value If it were "numerical value" or "value for people that only consider arithmetic to be mathematics", then I wouldn't even reply.

But "mathematical value"? No way. So many things people need to study in mathematics (like vector spaces) require a thorough understanding of the cardinality of infinite sets.

Firstly there is a difference between countably infinite sets (cardinality is aleph null) and uncountably infinite sets (cardinality is bigger than aleph null). The set of natural numbers is an example of a countably infinite set. And in these sets you can construct sequences that will "sweep" over the entire set and come up with a lot of great properties. A lot of proofs can be constructive. While in uncountably infinite sets, things become harder and proofs usually become non-constructive.

The irony is that in mathematics, just like how there are much, much "more" irrational numbers than rational numbers, you encounter a LOT of uncountably infinite sets. Like any basis of an infinite-dimensional Banach space (like the set of real-valued continuous functions on a compact space) is uncountable. But you want to solve problems and equations that require some properties from this Banach space. Then one thing leads to another and people spend A LOT of their time struggling with infinite sets. They have to develop methods and arguments that can apply to such objects.

>>9133590 >Second of all, the goalpost moving refers here to the logical fallacy you're committing. In this case, the trick of suddenly replacing infinity (all the various kinds that are actually defined and used in mathematics) with another, more specific concept. And it doesn't even help your case in any way, but it was just too cute not to point out.

No, that is clearly called taking things out of context when he refers to infinity as a concept, sperglord. The only thing that you prove is that infinity used in lower math is not really infinity, proving that infinity is a concept and not a number.

>>9133607 So in other words you guys all went autistic because it was clear the guy was talking about numbers, but accidentally used mathematics instead of numerical?

You should have just said that in the first place sperglord.

>>9133623 >To use the word 'mathematical value' is to invite a different kind of reply. If that rustles your jimmies, I'm pretty sure that makes you a sperglord, sperglord.

>Most people also believe in God >why do I feel like the arguments in this thread are just like arguing god does/doesn't exist? Because god is the same thing as absolute infinity

>The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute

>>9133630 Nah man, you're just spergging out over nothing. You can't expect people to know that mathematics is not the same as arithmetic, 99% of people probably don't know the difference. No reason to sperg so much.

Sometimes you forget and it felt like I was using the word number too much since I was talking about number systems. My deepest apologies for so deeply offending you anon.

>>9133654 Actually the absolute infinity guy is not me and I honestly don't know what that means.

Russell's paradox makes people have to think about the definition of sets (there have to be restrictions) and in ZF set theory there's no such thing as a set that contains all sets, or a set of all ordinal numbers.

Fussing over absolute infinity is a job for someone that either wants to replace ZF set theory or knows nothing about mathematics and ZF set theory.

>>9133666 >666 Devil worshiper, you have to turn to go to be able to believe in absolute infinity.

>The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute >-Cantor

>Firstly, there are different infinite sets. And I have to say I spend most of my time struggling with problems involving sequences, function series, nets, sets whose cardinality is bigger than aleph null.

Knowing that you're a graduate makes that even worse. Are you from Bumfuck University of Bumfucksville?

But he knows what he's talking about. You don't. Wait, did you think that because there are different kinds of infinity then some of them are less infinite? You are truly amusing.

>>9133778 Actually the bonus of being a mathematician is that you can tutor rich kids and receive money. Just don't join any institutions, which will always fuck you over, and do the administration yourself. Easy job, you already know all the materials. And people aren't ever gonna stop learning mathematics. You also have a lot of free time since you're mostly teaching the kids to think for themselves, not hold their hands.

With that much free time you can watch anime, learn Japanese, read physics books, learn more programming, read research papers, play games and enjoy life. So it's all good. People don't really understand what mathematicians do anyway. We can appear to be very hard-working while just lazing around when they're the ones that have to spend 8 hours at a office a day.

>>9133774 There's no topic anymore. What happened:

1. A person says some minor incorrect statement barely relevant to the topic. 2. A few people correct him. 3. Instead of acknowledging his error and moving on, he's trying to argue with them, saying increasingly more incoherent crap in the process. 4. Others join in. All-out flamewar.

>>9133816 You mean the 9001st thread where someone asks for some good textbooks? This is as bad as asking for anime recommendations. There is a already Google and a fucking wiki.

The wiki suggested stewart, just so you know... And google states almost no results for multivatiable. At most people saying: get this book or that book, but not giving reasons. Sorry

>>9133814 >1. A person says some minor incorrect statement barely relevant to the topic. >2. A few people correct him. You mean sperged and got offended >3. Instead of acknowledging his error and moving on, he's trying to argue with them, saying increasingly more incoherent crap in the process. You mean no one pointed out that he made an obvious mistake and sperged on other things. >4. Others join in. All-out flamewar. You mean people realized how much math majors are sperglords.

I mean seriously. The guy was just trying to make a point about 0s. And he even said that in certain fields you do calculations on infinity. This is like a Jew sperging that some guy fed him non Kosher shellfish, even though he knows that 99% of people only know that pork is not Kosher.

>>9133814 He clarified what he meant by saying infinity was a concept instead of a number. The mathfreaks just overreacted and didn't mention the difference between mathematical and numerical until after a million posts.

>>9133829 Here is the thing: I studied with some lame textbooks my own uni made. Then I read wikipedia to see if I missed anything, download what they learn at MIT and basically all the things I found on Google. But the crucial thing is to prove everything that is not a definition or axiom by yourself. I'm pretty confident I can solve almost every theorem or problem I've ever faced in college, even if I have mostly forgotten about them. Because I once solved them myself and I know how to look for the way.

I have not read all the textbooks in the world, nor do I have the time to. It's hard to recommend the best book when there are so many new things to learn instead of going back to topics you already know and try to compare textbooks written on it. You also DEFINITELY don't want to read the books I've read unless you're confident maths is your life. And definitely do NOT listen to what mediocre math students say on online reviews. There are good books that they just diss because apparently it's too difficult. A good math book is usually a challenging one and the more people that can understand it, the less challenging and eye-opening it is. This does not mean the hardest book is the best, sometimes it can be too obtuse and even wrong, but just keep in mind you don't want to listen to whoever says something is too hard for them, because there's a chance that guy's just dumb.

Thank you so very much for this post! I will keep all that in mind! For Calculus I I already got a not so easy, not so used book and it was pretty good, proving everything and all, not being dumbed down or anything. But indeed math is not my life, I'm studying engineering, actually, so... I just didn't want to plug numbers into formulas I don't even know the origin.

>>9133877 Nodoka had previously taken the strawberry from Yui’s cake. I believe Yui offered Nodoka a piece of her cake but had not expected Nodoka to go straight for the strawberry. This upset her greatly and she made a big deal about it by calling everyone asking for their opinion on the strawberry so as to prove to Nodoka that the strawberry is the most important part of the cake. In the same episode, Mugi is jealous of the intense bond between Ritsu and Mio. She thinks the fact that Mio hits Ritsu on a regular basis is proof of their closeness. She asks Ritsu to hit her, but Ritsu can’t bring herself to do it. They spend the rest of the episode trying to get Mio to hit Mugi, but everything fails. Then Mio gets the idea of stealing Mio’s strawberry (since it was made to be such a big deal, she thought that must work). If I recall correctly however, Mio did not hit Mugi over it, but rather just got very sad and was pretty shocked. In the end Mugi and Ritsu explained what was going on, and then Mio was going to hit Mugi… I don’t think she could hit her either, though.