matt grime

The gamm function is used in stats: the sum of poisson distributions is a gamma dist, i seem to think. Well, in any case, mutatis mutandis that is correct. It also gives a functional relationship for the riemann zeta function that allows us to deduce where the poles of the analytic continuation are. (Used in some parts of physics that care about random matrix theory. see work of Jon Keating and MIchael Berry).

You should also have the "I got a reply from Matt when he'd not had any coffee yet that morning and was a shirty little sod".

You see, this is why maths should be taught properly at school. We are not saying the apples are equal, or not eqaul. We are saying things about the NUMBER of apples, not the apples themselves.

"Theorems on the Limits of Functions" - sounds like there could be a book of 'em, and old one written by Hadamard or something.

Look, Daymare, mathematics *is* an abstract subject. If reality does diverge from a model then the model is wrong not the underlying mathematics that are independent of the use in the model. Deal with it. Stop trying to use unmathematical arguments to cast shadows on mathematics itself. 1+1=2 is, frequently, the definition. There is no fallacy in the mathematics, even if there were a fallacy in the model which originally motivated it. What on earth in reality is 1? Platonism is not very popular in mathematics. So get a new model if you're that annoyed with it, but leave mathematics alone, please. If you are going to introduce the axiom that x =notx, then you'd better state in what axiomatic system you're operating. I mean, is x a group element, a vector space, a set, a proposition??? It's just meaningless nonsense.

Damn, I've been doing my mathematics with numbers and not apples. Wonder if they'll revoke my BA? But I guess that's the problem when they don't teach degree level maths from first grade books.

0 is defined in this case as the additive identity in a ring. Your notion of regulating infinity is also an analytic one (removable singularity, pole of degree n, essential singularity, as you well know). We may certainly write 1/0 = [math]\infty[/math] if we are operating on the complex sphere, but we aren't. Moreover, when we say that, say, sin(x)/x is 1 when x is 0 we are making several assumptions that merely boil down to the fact that as a function on R\{0} it has a continuous extension onto the boundary, we are not actually defining 0/0 in any absolute sense. We are not saying something about the arithmetic of the real numbers but about functions of a real variable. I'm glad you feel that you can compellingly make such absolute claims as you have about the origin of maths/physics, though I disgree with some of your conclusions. I don't think we should dismiss L-functions as mere integrals that casually. Nor did I claim the cases I gave were the first use of these "pure" things (RSA, though it is the manner in which we use groups and rings that is important, not counting things. I could also cite groups originally arising in a study of roots of polynomials that now has implications in electrical and chemical engineering), however it seems that nothing I can offer will satisfy your (unstated) requirements - whatever the origins of the motivation of a field of study the abstract study of other things can and is useful in it. Hamiltonian dynamics almost certainly predates the formal notion of a "closed non-degenerate two form on a manifold", but that doesn't stop that bit of "pure" mathematics being useful. I would accept some of these opinions if you could for instance categorically show that nothing produced in the abstract study of these objects has ever had any influence or bearing on the applications. I could also add in about discrete mathematics and logic and their use in computer science. The underlying influences in mathematics have shifted over the years, oringinally homological algebra arose from astronomy, and hence why there are syzygys (not that I think I've spelt it correctly). The second half of the 20th C saw a shift away to abstract study in its own right and now we're seeing the physicists, with string theory in particular, come back and give new impetus to maths. That is only a good thing. Pure mathematicians aren't as stuck on rigour as you seem to think we are, but once we've got a piece of maths sorted then we tend to get itchy about people misunderstanding it. (And, no I don't mean you. You evidently don't fall into that category.) Actually I would hold that by treating infinite sums in such a formal way (ignoring convergence issues) is a good thing (pure mathematicians do it all the time). After all the model is just that, and anytime something like 1/0 appears it is not the "fault" of the underlying mathematical object, but in its application if we were trying to avoid an infinity.

Then why did you stoop to his level if you thought his attacks unjustified? Pointing out where someone's ideas are wrong is not the same as calling them an asshole, or, in the case where you refer to me, a "little asshole" I presume. Surely as soon as mathematics gets a use it becomes, by its use, "unabstract"? Modulo arithmetic is a good example of pure mathematics that has found a use - abstract ring theory becomes RSA. How about the Riemann Zeta function? Abstract number theoretic object that appears to be of interest in describing energy levels in some dynamical system or other. Symplectic geometry and quantum field theory? Triangulated categories and string theory (though if you're of the experimentally verifiable school that's a little bit rubbish, isn't it?). Lyapunov exponents and choatic systems? Functional analysis and probability theory? Look at Rietz's representation theorem for something ugly and pure that probability people care about. Assuming prob/stats counts as real world. We study it because it is interesting and who knows, maybe one day someone cleverer than us will put it all together and figure out something it is good for - Raul Bott started off as an electrical engineer and realized that he needed to understand differential geometry and ended up becoming an outstanding (pure) mathematician. Though I think we're starting to see a move away from such artificial and unhelpful labels. My prejudice is that the issue of what 1/0 is or isn't, and why it isn't defined are that the question is almost always ill-posed. You may treat it in many ways, as physicists are wont to do (treating divergent series by approximating by the first few terms, for instance) that work out. That doesn't alter the fact that the question was probably ill-posed and knowing about the axiomatic structure of mathematics simply explains why it doesn't work within the real number system (ie a field), but multiplication by 0 is consistently defined within this axiomatics framework. I apologize if it appears i misread your post - I almost certainly did. You did certainly say this though: "But in the opinion of a physicist 0/0=1 is the most sensible choice" and the question is about mathematics since that is where we refer to it as undefined.

Then why did you stoop to his level if you thought his attacks unjustified? Pointing out where someone's ideas are wrong is not the same as calling them an asshole, or, in the case where you refer to me, a "little asshole" I presume. Surely as soon as mathematics gets a use it becomes, by its use, "unabstract"? Modulo arithmetic is a good example of pure mathematics that has found a use - abstract ring theory becomes RSA. How about the Riemann Zeta function? Abstract number theoretic object that appears to be of interest in describing energy levels in some dynamical system or other. Symplectic geometry and quantum field theory? Triangulated categories and string theory (though if you're of the experimentally verifiable school that's a little bit rubbish, isn't it?). Lyapunov exponents and choatic systems? Functional analysis and probability theory? Look at Rietz's representation theorem for something ugly and pure that probability people care about. Assuming prob/stats counts as real world. We study it because it is interesting and who knows, maybe one day someone cleverer than us will put it all together and figure out something it is good for - Raul Bott started off as an electrical engineer and realized that he needed to understand differential geometry and ended up becoming an outstanding (pure) mathematician. Though I think we're starting to see a move away from such artificial and unhelpful labels. My prejudice is that the issue of what 1/0 is or isn't, and why it isn't defined are that the question is almost always ill-posed. You may treat it in many ways, as physicists are wont to do (treating divergent series by approximating by the first few terms, for instance) that work out. That doesn't alter the fact that the question was probably ill-posed and knowing about the axiomatic structure of mathematics simply explains why it doesn't work within the real number system (ie a field), but multiplication by 0 is consistently defined within this axiomatics framework. I apologize if it appears i misread your post - I almost certainly did. You did certainly say this though: "But in the opinion of a physicist 0/0=1 is the most sensible choice" and the question is about mathematics since that is where we refer to it as undefined.

It isn't a sensible choice, it is a ridiculous choice and you're making the same mistake a lot of people make in dealing with limits. Actually, more than usual. Firstly we only deal with limits that exist within the reals - saying the lim1/x, as x geoes to 0, is infinity means exactly that it does not exist and cannot be used as a number like you're doing. secondly, when you write, lim/lim you are treating something that isn't a real number as a real number. And you're not even letting the x differ in numerator and denominator and act independently as one should in these cases. If you want to do calculus stay in the reals (or complex, or even p-adics), if you want to do artihmetic with transfinite numbers can I suggest you read up on it first? Your ad hominem attack on Homunculus seems odd and misdirected and unmathematical, and as this is maths, and not real life (your ideas of what maths is good for seem very odd and uninformed, not to say antimathematical, so why post in a maths forum?), one wonders what the point of it is.

It isn't a sensible choice, it is a ridiculous choice and you're making the same mistake a lot of people make in dealing with limits. Actually, more than usual. Firstly we only deal with limits that exist within the reals - saying the lim1/x, as x geoes to 0, is infinity means exactly that it does not exist and cannot be used as a number like you're doing. secondly, when you write, lim/lim you are treating something that isn't a real number as a real number. And you're not even letting the x differ in numerator and denominator and act independently as one should in these cases. If you want to do calculus stay in the reals (or complex, or even p-adics), if you want to do artihmetic with transfinite numbers can I suggest you read up on it first? Your ad hominem attack on Homunculus seems odd and misdirected and unmathematical, and as this is maths, and not real life (your ideas of what maths is good for seem very odd and uninformed, not to say antimathematical, so why post in a maths forum?), one wonders what the point of it is.

Try counting: fix one element, say one of the pluses. Then you wish to know how many ways of writing the other elements, which is I believe 7choose3, as we only need to count the orderings relative to the fixed element.

Try counting: fix one element, say one of the pluses. Then you wish to know how many ways of writing the other elements, which is I believe 7choose3, as we only need to count the orderings relative to the fixed element.

"Fullness is represented by an infinitely_long_(totally_pointless)_solid_element model." That doesn't actually state what it is though, does it? Only a representation of it, whatever it might be.

"Fullness is represented by an infinitely_long_(totally_pointless)_solid_element model." That doesn't actually state what it is though, does it? Only a representation of it, whatever it might be.

actually you increase the number of cases to check (obviously) if you allow three truth values. AI uses lots of models of logic (neural nets, fuzzy etc) and there are whole journals dedicated to them. Note to Doron. In category theory there is a category of categories, if one is careful.

actually you increase the number of cases to check (obviously) if you allow three truth values. AI uses lots of models of logic (neural nets, fuzzy etc) and there are whole journals dedicated to them. Note to Doron. In category theory there is a category of categories, if one is careful.

yep, correction to me, the LHS isn't what I sad. Note that the LHS is purely imaginary and the RHS purely real, thus there are no solutions except the trivial one, z=0, assuming z' means conjugate.

yep, correction to me, the LHS isn't what I sad. Note that the LHS is purely imaginary and the RHS purely real, thus there are no solutions except the trivial one, z=0, assuming z' means conjugate.

More opinions on mathematics, no facts, definitions or proofs.... wonder where we've seen this before.... Set theories do not ignore what you might mean by fullness, it is simply not a set in that theory (here I mean the mainstream ones), but a proper class. The collection of all sets (in some theory) is not a set in that theory. And? A vector space is a collection of vectors, but not itself a vector. Sorry you don't care to understand set theory, but that's not our fault, so please stop bombarding people with your misinterpretations of mathematics.

More opinions on mathematics, no facts, definitions or proofs.... wonder where we've seen this before.... Set theories do not ignore what you might mean by fullness, it is simply not a set in that theory (here I mean the mainstream ones), but a proper class. The collection of all sets (in some theory) is not a set in that theory. And? A vector space is a collection of vectors, but not itself a vector. Sorry you don't care to understand set theory, but that's not our fault, so please stop bombarding people with your misinterpretations of mathematics.

What does that dash mean? (z'^9) Presumably complex conjugate. LHS is 2*Im(z^9) which, if z is re^(i\theta), is 2r^9sin(\theta), and that equals 9r^4.

What does that dash mean? (z'^9) Presumably complex conjugate. LHS is 2*Im(z^9) which, if z is re^(i\theta), is 2r^9sin(\theta), and that equals 9r^4.

what's your inkling? do you think it true or false?

what's your inkling? do you think it true or false?