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  1. S

    Klein bottle

    Thanks a lot Hurky for your explanations .. I guess I am discussing a topic which I dont really understand about . I still am curious why a sphere squished at 2 opposite points would eventually give a singularity , but if squished on all points ( which would result in the formation of a...
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    Klein bottle

    I could not understand what you are saying completely . I tried looking up what a covering space was but I didnt understand much in the definitions as they were framed in mathematical language. Anyway from what you have said I assume that a covering space is something like a mapping from one...
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    Klein bottle

    Ok .. so going by this you would like to say that the mobius strip has all points as 'singularity' ?? Hence the laws of physics as we know them are no longer valid in this mobius strip. Well I just think we should be open to two different perspectives, or strings of thought . First ...
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    Klein bottle

    Yes , I can see that a sheet of paper is not a perfect analogy and the 2 points on 2 different sides are distinct if we look at them as being part of a paper . I also agree with you that if the strip of paper were of 0 thickness and it was transparent also lets say , the 2 points on opposite...
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    Klein bottle

    Thank You Hurky and Simpson very much for giving nice examples and helping understand the things . But I disagree that when you go round the mobius strip once , the shape disorients. I feel that by going round the strip once would not leave you in the same place . You have 2 go round the...
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    Klein bottle

    Can anyone explain in laymans terms what a Kleins bottle is . I have encountered the definition that it is a non orientable surface , that it is a 2 dimensional manifold in 4 dimensions. I dont have a clue what a non orientable surface is , or what a manifold is . I also dont have any idea...
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    What is Riemann zeta function.

    Thanks very much for the explanation. But there are some doubts which persist for me . You say that I should use the definition of Riemann function on the positive real axis , and extentd the definition for complex numbers . But the thing is that I was only able to find the definition for...
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    What is Riemann zeta function.

    Well , I think I have understood something wrong , because I can think of many examples of functions that are completely differential in a domain , but there exist more than 1 continuation of that function over a larger domain, which is still differentiable. eg. f (x) = 1/ x^3 and f(x) =...
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    Did Paul Cohen settle the Continuum Hypothesis?

    I would like to ask from where did the axioms of ZFC come from in the first place ? Why is it that you consider the axioms of ZFC relevant , but adding a few more axioms to ZFC , just an exercise for set theorists ? I am not a mathematician , and have very limited knowledge of mathematics...
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    What is Riemann zeta function.

    By the way can we not represent the Riemann zeta function over the larger domain with the help of some power series ?
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    What is Riemann zeta function.

    Well , after looking at a couple of places , I came to know that the analytic continuation is a function that has the same value as the given function within the given functions domain , but is defined at points in a larger superset of the original domain too . Also that the analytic function is...
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    What is Riemann zeta function.

    Could anyone tell me what is the Riemann zeta function. On Wikipedia , the definition has been given for values with real part > 1 , as : Sum ( 1 / ( n^-s) ) as n varies from 1 to infinity. but what is the definition for other values of s ? It is mentioned that the zeta function is the...
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    Euclid's Proof

    In the proof , it is not that p1 , p2 , p3 have been replaced by powers of 2 . All that it is saying is that : p1.p2.p3.p4.....pn < 2 . (2^2) . (2^4) .... ( 2 ^ (2^n - 1 ) ). This is because it is assuming the theorem to be true for p1 , p2 .. upto pn .
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    F(x)≡0 (mod 15) Find all roots mod 15

    why at all should mn divide f(x) ????? consider f(x) = 18 , thus possible values for m and n are 6 and 9 , but clearly 6 x 9 = 54 does not divide 18 , but had m and n been coprime then we would have a completely different answer.
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    Why doesnt Bertrand's postulate imply Legendre's conjecture?

    It looks to me like your proof that legendre implies andrica , is implicitly assuming that there are 2 primes between n^2 and (n+1)^2 . But Legendre guarantees only the existence of a minimum of one. If there is only 1 prime bw n^2 and (n+1)^2 , then I am unable to follow how you conclude that...
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    What distribution should i use?

    The question doesn't seem to be clear . I assume there are only 2 outcomes to a bet - win or lose . Now you say that no more than 1 player can win the bet , but how can that be : If player 1 makes the bet , and then player 2 and player 3 accepts the bet , but player 4 declines . If player 1...
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    A seemingly simple combinatorial problem

    I don't get it , why should the answer be r+p-1Cp-1 , if the coefficients are different . Consider : a + b = 5 There are 5 nonnegative integer solutions Now consider : a + 2b = 5 the only solutions that a can take are 1,3,5 - only 3 solutions .
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    Books on tensor analysis

    Thanks a lot .. I had a peek at "A brief on tensor analysis" by Simmonds on google books ... it seems like the book I'm looking for ... looks like it is concise .. and by the contents .. the 1st chapter seems to be vectors , and the last chapter seems to be about curl divergence , gradient etc...
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    Books on tensor analysis

    Hi All , I am looking for a book on introduction to tensor analysis . I do not have much of a background in mathematics .. I have an undergraduate degree in engineering . My aim is to understand General Relativity ... I would also like to understand Quantum Mechanics ... It feels odd that...
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    Algebra help please

    Thank You very much Elucidus for the PDF link ... the steps involved seem very simple and clear (for the cubic equation ) ... but who would have thought to do those steps in that way ... not me anyway !
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    Deal or No Deal

    Thank Goodness .. at least we are getting somewhere .. So you have agreed that at the end each card (or ticket) has equal odds of being the ace or a winner. Now let us see where that leads us .. There are 2 cards - each has equal odds .. what does that mean --- each of these cards has a...
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    Use limit definition to prove

    I am not very familiar with the delta epsilon proof , but is it not sufficient to show that for a given delta you can find an epsilon , do we need to show the opposite ?
  23. S

    Points on a plane

    Yes agreed that the function in this case is not continuous , but it is easy to see that the function ( the function I am talking about is the difference of no. of points on one side of the line to the other) shall take integer values between -2n and +2n . It is also seen that the function has...
  24. S

    Points on a plane

    You can look at the following link ...
  25. S

    A couple of Infinite Series questions

    Ok .. I got how to find the sum : \sum_{r= 1}^\infty \frac{1}{2r(2r+1)} \sum_{r= 1}^\infty \frac{1}{2r} - \sum_{r=1}^\infty \frac{1}{(2r+1)} Now consider the series expansion of log(1 + x ) and in this expansion...
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    A couple of Infinite Series questions

    Thanks again .. what a fool I was .. Rather than considering the area under the curve from i to i+1 , I was considering the area under the curve from i-1/2 to i + 1/2 , thats why I had to take the difference and check for monotonicity and all ... it was pretty obvious . By the way Ubibic ...
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    A couple of Infinite Series questions

    Thanks Robert for the explanation . Yes I was able to show that \sum_{i=1}^r 1/i > \int_1^r\frac{1}{r} =ln(r) But what bothers me is that I had formed some sort of argument in my mind to convince myself that if the integral is bounded for some function f(x) then the sum shall also...
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    A couple of Infinite Series questions

    Well I just came to know that \sum_{r=1}^\infty 1/r is itself divergent , so I am unsure of your question , it looks like some - \infty + \infty problem . I am at loss to see whats goin on ... does it mean the sum is undefined (because it doesnt seem to be right to say that the sum is...
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    Improper Integral

    Yes the integral doesn not converge . This can be seen without integrating - the function 1 / (x * ln x) goes to infinity at x = 1 , and also func is continous in the interval .. so the area under the curve is infinite
  30. S

    A couple of Infinite Series questions

    If the sum is for values of r from 0 to infinity , then the 1st term in your second question is -infinity. So how is the sum supposed to converge ??
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