arsmath
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Registered User
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May 18 |
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Calculate the tendency of a set of samples These are pretty close to the same thing -- the beta coefficient from the regression can be written in terms of the correlation -- so there's not much to choose from. The question of what makes a good model for your application depends on your application. I would have to think there's a large medical literature on modelling normal and abnormal heart behavior, so I suggest looking there. |
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May 10 |
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Why/when classification of simple objects is “simple” ? E.g. (unknown) classification of simple Lie algebras in char =2,3… There seems to be some dividing line where tightly constrained cases have a series/sporadic structure, and relaxing the constraint too much destroys this. For example, the classification of finite simple Moufang loops adds one additional series to the list of finite simple groups, while relaxing this slightly to Bol loops destroys any chances of classification. |
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May 8 |
awarded | ● Notable Question |
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Apr 30 |
revised |
Cofibrant replacements of a given object in a combinatorial model category Add model categories tag. |
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Apr 23 |
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General Theory of Left-Exact Localization? Thanks, Ricardo, that does help. (The terminology is slightly different than I used above, so if anyone is curious it's section 5.6.) |
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Apr 23 |
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General Theory of Left-Exact Localization? I don't see where Krause addresses left-exactness. |
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Apr 23 |
asked | General Theory of Left-Exact Localization? |
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Apr 5 |
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How to refer to a theorem that you have shown to be wrong I would go with a neutral term. I suggest "claim". |
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Apr 2 |
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Was the early calculus inconsistent? I don't agree with the opening paragraph of this answer. "Consistent" is a perfectly clear English word that means, in this context, "not self-contradictory". If a person is inconsistent, they are not saying or doing the same things over time. |
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Mar 20 |
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Cosheafification It's way up there in the hierarchy. Vopenka himself thought it was false -- that's why he proposed it as an argument against the largest of large cardinal axioms -- but I think most set theorists think it's independent. Even if it's fine, it means that you're saying you have no control over the size of cosheafification: it could turn a countable set into a set of cardinality so large that it dwarfs all sets that appear in day-to-day mathematics. |
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Mar 19 |
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Cosheafification Your easier-to-check version of the adjoint functor theorem relies on a large cardinal axiom, which is therefore not provable in ZFC unless ZFC is inconsistent. |
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Mar 14 |
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one “big” Hilbert scheme? I think he means so that he can accept it as the answer. |
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Mar 14 |
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Calculate $Hom$ in derived category fix latex |
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Mar 9 |
awarded | ● Nice Answer |
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Mar 5 |
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Where in ordinary math do we need unbounded separation and replacement? Game theory is not ordinary mathematics? Gale-Stewart games arose as an attempt to extend the determinacy of finite-length zero-sum games to infinite games. David Gale was a mathematical economist who's most famous for the Gale-Shapley stable matching algorithm that helped Shapley win the Nobel Prize in economics. Once determinacy of Gale-Stewart games for open and closed sets was shown, it's a natural question to wonder if it holds for sets higher in the Borel hierarchy. The theory of infinite games just turned out to be really, really hard. |
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Mar 3 |
accepted | Market-clearing price vector in an “aggregate demand system” |
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Mar 1 |
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a problem in functional analysis that erdos solved in 2 lines This should be closed in favor of the stack exchange question, in light of the quality of the answers there. It's hard to do much better than have the actual source of the anecdote answer. |
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Mar 1 |
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Market-clearing price vector in an “aggregate demand system” It's not a convex optimization problem, so you can't plausibly solve a problem with a million variables, but for problems with 20 variables, non-convex solvers will work. Google "Computational General Equilibrium" for more information. |
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Mar 1 |
awarded | ● Nice Answer |
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Feb 28 |
answered | Market-clearing price vector in an “aggregate demand system” |
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Feb 13 |
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Mathematicians whose works were criticized by contemporaries but became widely accepted later And then two years later, computer scientists figure out how to promote the assistant to the boss, and now that mathematics has been automated, all human mathematicians become instantly obsolete. Alternate scenario: thanks to the proof assistants, the world's supply of constructive theorems can be supplied by one guy in his basement and constructivism dies as an active research project. Since constructive proof assistants are a solved problem, all of the grant money in computer science goes to the unsolved problem of proof assistants for ZFC. |
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Feb 12 |
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Mathematicians whose works were criticized by contemporaries but became widely accepted later Intuitionistic logic is of mathematical interest. Some things are intuitionistic, the way some things are nonabelian groups. |
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Feb 12 |
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Mathematicians whose works were criticized by contemporaries but became widely accepted later Is this true? Of course not everyone is going to switch mathematical styles instantly, but was there any actual resistance? (The evidence that Paul Gordan said anything like "That is not mathematics, that is theology" is pretty thin.) |
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Feb 12 |
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Mathematicians whose works were criticized by contemporaries but became widely accepted later Grothendieck is as far from a plausible example of this phenomenon as can be imagined. He won the Fields Medal in 1966. I'm sure there were people who didn't like Grothendieck's influence and style of doing mathematics, but the only reason they would care is that he was so influential. |
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Feb 12 |
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Mathematicians whose works were criticized by contemporaries but became widely accepted later Yes, yes, yes, and 1/2 yes. (How do you formalize classical mathematics in Martin-Lof type theory? Doesn't strong normalization prevent it?) My point is that unless you are a constructivist, Martin Lof type is just another thing you can study, like complex analysis, or homological algebra, or whatever. People who study the fundamental groups of hyperbolic 3-manifolds don't make fun of 19th century complex analysts. There's no reason why type theorists of the 22nd century need to make fun of today's set theorists. |
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Feb 12 |
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Mathematicians whose works were criticized by contemporaries but became widely accepted later This will never happen. There's no trade-off between ZF and Martin-Lof type theory, unless you are explicitly philosophically committed to constructivism. As a proportion of mathematicians, classical complex function theory is a much smaller proportion of mathematics than it was in the late 19th century, but nobody makes fun of complex analysts. |
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Feb 11 |
answered | Where in ordinary math do we need unbounded separation and replacement? |
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Feb 11 |
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Where in ordinary math do we need unbounded separation and replacement? Borel determinacy is a theorem in real analysis, and therefore part of "ordinary mathematics". Maybe it's not an important theorem in real analysis, but it is indisputably a theorem in real analysis. |
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Feb 9 |
answered | Differential geometry study materials |
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Feb 1 |
awarded | ● Yearling |
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Jan 31 |
accepted | Are integers real? |
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Jan 29 |
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Are integers real? The best introductions to type theory are more computational oriented than math oriented. I would recommend Girard's "Proofs and Types", which is available online. I don't know a good reference explicitly for the definition of the reals inside a type theory. The main consumers of type theory tend to be more interested in constructive mathematics than in a non-constructive topic such as classical analysis. Second-order arithmetic (en.wikipedia.org/wiki/Second-order_arithmetic) is like a type theory with two types, even though it is couched in set-theoretic language. |
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Jan 29 |
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Are integers real? There is a gigantic mathematical theory of types, that predates the invention of the computer, and has had considerable influence on the design of programming languages such as ML and Haskell. Some people would like to replace set theory with type theory. I think the idea of one replacing the other is pointless, since for most mathematical applications I can express anything I want to say equally well in either. |
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Jan 29 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? You're right, function classes is probably a better way to put it. |
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Jan 29 |
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What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? You do indeed have a pairing operation in TG. |
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Jan 28 |
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realcompact space I don't know much about the subject, but the Gillman and Jerison "Rings of continuous functions" is a good book in general. |
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Jan 28 |
answered | What kinds of operations are well-defined when working with sets, classes, conglomerates, and yet higher order collections? |
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Jan 28 |
answered | Are integers real? |
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Jan 28 |
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Concise model of modern fiat money and its non-conservation And this comes to the critical point: at no point in the workings of the system are any balance sheet rules violated. The Fed balance sheet works like the balance sheet of any other bank. Having 100 dollars of Fed money is like having 100 dollars in a checking account -- in either case it's a liability that requires a matching asset. What makes the Fed special is that the ordinary bank has be able to convert the check into Fed money, which it can't make more of. The Fed can. |
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Jan 28 |
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Concise model of modern fiat money and its non-conservation @Greg No, the Fed literally does hoard widgets, in the form of "Treasury bonds". <i>Theoretically</i> it could hard anything. <i>Theoretically</i> the asset side of the Fed's balance sheet could be anything. There's nothing in the notion of central bank fiat money that requires the asset side to be anything. |
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Jan 28 |
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Concise model of modern fiat money and its non-conservation @Greg Okay, I see. I hadn't heard of the idea that all money could be traced back to Fed lending. |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation I don't get where you get this "money is lent from the central bank" idea. If you have money, it's your money -- you're not supposed to give it back to the central bank some day. In the Monopoly money analogy, the bank doesn't lend you money, it gives you money, and you give it a hotel you built on Park Place. |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation I'm with Steve -- I don't see what's so mysterious. There's no theoretical reason why a central bank couldn't operate with a hoard of refrigerators. The Fed could print up money, and use it to buy baseball cards, or gourmet yogurt stands, or slivers of the True Cross. The mystery is not what the Fed does, but what everyone else does. What determines the value of the money that the Fed prints, and why is that value nonzero? |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation The Fed holds Treasury bonds, which pay interest. The Fed also makes money for services it provides to the banking sector, such processing checks. It also makes loans. All told, it takes in more money than it spends on wages and expenses. This difference it rebates to the Federal government. |
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Jan 22 |
answered | Mathematics with the negation of AC |
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Jan 16 |
accepted | Structure of f.g. modules over a non-commutative ring |
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Jan 16 |
answered | Structure of f.g. modules over a non-commutative ring |
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Jan 13 |
answered | Difference between ‘generalized gradient’ and ‘subgradient’ ? |
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Jan 13 |
revised |
Small Implications of the Axiom of Replacement added 57 characters in body |
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Jan 13 |
asked | Small Implications of the Axiom of Replacement |
