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    Problem in proving d(x,y)=0 implies x=y.

    Hello everyone. I am trying to prove that the in a planar domain U \subseteq C equipped with a metric \rho, the definition of the distance between P and Q, both lying in U is given by \\ \\ d_{\rho}(P,Q)=inf \left\{ L_{\rho}(\gamma): \gamma \in C_{U}(P,Q)\right\}, where C_{U}(P,Q) denotes all...
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    A complex problem

    Hi all. The problem is "Prove that a function which is analytic in the whole plane and satisfies an inequality |f(z)| < |z|^n for some n and sufficiently large |z| reduces to a polynomial." I do not understand what I need to show that the function reduces to a polynomial. Any help will be...
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    Differentiability and Continuity

    Earlier when calculus was invented by newton and leibniz, then such questions of rigor was absent, or they did not have the right tools for the precise definitions of continuity, until weierstrass. But then as mathematicians looked carefully at these concepts, they were not satisfied with just...
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    Mobius maps form a Simple group

    hi guys, plz help.
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    Bolzano's Theorem

    So the proof involves bisection of the intervals. We start with interval [a,b], where f(a)>0 and f(b)<0. Now we bisect the inteval and consider f((a+b)/2). If the function value at the midpoint is +ve then we select the interval [(a+b/2),b], else the interval [a,(a+b)/2]. So in this way we get a...
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    Bolzano's Theorem

    The Bolzano theorem, which is a special case of intermediate value theorem, states that if you have a continuous function on an interval [a,b], such that f(a) is positive and f(b) is negative, then there must exist a point "c" belonging to the interval (a,b) where f(c)=0. Continuity is...
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    Mobius maps form a Simple group

    Hi all, How do I prove that the set of all Mobius Maps form a simple group, that is they have no non-trivial subgroup? How can I characterize a non-trivial subgroup? Hints will be welcome. Thanks
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    Galois Extension of Q isomorphic to Z/3Z

    Hi... How do I construct a Galois extension E of Q(set of rational numbers) such that Gal[E,Q] is isomorphic to Z/3Z. Thanks.
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    Isomorphism in graphs

    Oh yeah, I got the point. Thanks for the help.
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    Isomorphism in graphs

    Hi all, If I have to prove that the graph G and its complement G' are isomorphic, then is it enough to prove that both G and G' will have the same number of edges. Intuitively its clear to me, but how do I prove this. If there's a counterexample, please post. Thanks in advance.
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    Icm 2010

    Hi Guys, no reply! :-( I hope the question is pretty clear.
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    Icm 2010

    (Well I don't know if this post should be here or not. If not please move it to the appropriate place.) Hi Everyone. Next year International Congress of Mathematicians will be held in Hyderabad, India. And I am 2nd Yr undergraduate student in mathematics, and I wish to attend it. The thing I...
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    Explain the difference between these square roots

    And also because that we wish that square-root should be a "function", and for being a function it has to be defined like that only. By definition, a function takes a value from a set A and maps it into B, and no two numbers in A can map to the same number in B.
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    An integer between n and n+1 where n is an integer.

    thanks buddies..I will surely try to get my hands on the book.. by the way, why was the last post deleted that gave a proof to my question?? Was that proof okay?
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    An integer between n and n+1 where n is an integer.

    Well, I have just passed my high school and will be going in undergraduate course this year. therefore i don't know Peano axiom in detail. I think i have to study abstract algebra.Will that help me? Also, can i have a suggestion of a good introductory book treating the subject in detail as well...
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    An integer between n and n+1 where n is an integer.

    hmm..well and how the integers are exactly defined? I mean they are just the set of all natural numbers , with their negatives and zero. Is there any abstract way of defining them? Please describe in bit more details. thanks.
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    An integer between n and n+1 where n is an integer.

    hi guys.. Does this statement require a proof? It seems pretty obvious to me. "prove that there is no integer between n and n+1 where n is an integer." Also if it does require a proof, what I need to show? Just few hints will suffice. thanks jitendra
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    Colourful space

    I don't know how to approach it...but know that it is based on the concept of denumerability of real numbers. I don't want complete help but just few hints so that i can do it myself.plz help. thanks
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    Colourful space

    Hi everybody, I am unable to tackle this problem, and don't know how to attack it. can someone plz help me how to attack the following problem. Q. Suppose colour every point in 3-D space is assigned one of the three colours- red,green,blue.Can i conclude the following???: 1)there must...
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    Any Hints .

    sorry y=arccos z.(instead of arccos x)
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    Any Hints .

    Any Hints plzzzz. hey guys can u plz give a few hints on how to solve the following diff equation--- y' = 1 + x.(cos y)^2 I have tried the substitution y = arccos x but it does not work. plz help me. thanks in advance.
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    Can a field disturb the geometry of a space?

    But i haven't mentioned about gtr in my first paragraph? It's "electromagnetic field".
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    Can a field disturb the geometry of a space?

    No Chris. I wasn't offended. I'm really thankful to u to hear my questions and reply to them. I tried to find some hidden mistakes but really couldn't find it. I shally be very grateful if u could point out the errors and I may then find the solution. thanks.
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    Can a field disturb the geometry of a space?

    Yeah I may not be albert einstein but he is my role model. And i don't think that asking such (silly) questions will tarnish him. the quetion was indeed asked in an another forum (ww.orkut.com). and i answered the question asssuming the Presence of gravitational field. I was unsure if the...
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    Can a field disturb the geometry of a space?

    Ok.. "Since every point on the field line is a photon which in turn is occupying a point in space. This makes the space non-euclidean, since there cannot be defined any straight line on this space and surely in euclidean space straight lines do exist." But I can take any two points in the...
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    Can a field disturb the geometry of a space?

    this means that the presence of a gravitational field will also distort the geometry. and I didn't understand the last line--"and you are using "quantized field in an unusual way." Is the assumption that the field is quantized imply any condition in the answer? Also does the geometry the...
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    Can a field disturb the geometry of a space?

    hI guys. Back after a vey long time. The question is-"Consider a 3-d surface on which normal Euclidean geometry is valid. Now assume that electromagnetic field is allowed to pervade the whole of the surface . Now what is the possibility that the geometry of the space will be non-euclidean, if...
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    Mass in Relativity

    This is exactly what I wanted to know that how momentum is exactly defined in QM.Thanks guys I suppose I have got an answer to the question.
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    Mass in Relativity

    Ok then. what should be the correct answer to my question posted - "Can we mix SR and uncertainty principle? for ex. from uncertainty principle we have \Delta x \Delta p \geq h/4\pi Books then write m \Delta x \Delta v \geq h/4\pi with an assumption that m can be measured accurately...
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    Mass in Relativity

    But my question reamains unanswered! As in post #8 "By that I suppose that mass is a scalar qty and hence invariant. But the relativistic mass is just due to relative motion between two observers. But then how mass is defined in SR and QM and GR ? Is the definition of mass taken the same in...
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