Can anyone explain the Mobius Continuum or the Mobius Strip to me?
612917
Very roughly a surface is orientable if it has two sides so that, for example, is it possible to paint it with two different colours. A sheet of paper or the surface of a sphere are examples of orientable surfaces. A Mobius strip is a non-orientable surface: you can build one with a strip of paper (twist the strip and glue end together to form a ring) and verify that it has only one side: it is not possible to paint it with two colours.
1161312
To the best of my knowledge.The point is a well defined mark. It can be located anywhere in space and its position can be specified excatly wrt some co ordinate system. So it is not undefined.\nHowever the other 2 elements have one thing in common and that is we cannot specify the dimensions of any of them. In other words each of them can be extended to infinite dimensions.
424650
Not really enough information to help, so try this site:\n\nhttp://www.blc.edu/fac/rbuelow/calc/ex4-6.html\n\nit's the second problem down the page
126093
A one-sided piece of paper is a Mobius circle.  They're easy to make.  Take a strip of paper about 1' wide by 11" long.  Put the ends together, but not like a simple band - TWIST one end, so the backside of the piece of paper on one end, is joined to the front side of the other end.  Tape or glue them together.  The piece of paper now has only one side.  the inside of the circle flows to the outside, and back to the inside again in an endless surface.  Try it!
991775
Cantor used a diagonalization argument. We show that the open interval (0,1) is uncountable.  Suppose that f:N->(0,1) is any function. We how it cannot be onto by constructing an element of (0,1) that is not in the image of f. Write the decimal expansions\n\nf(1)=.a_11 a_12 a_13 a_14 .....\nf(2)=.a_21 a_22 a_23 a_24 ....\nf(3)=.a_31 a_32 a_33 a_34 ...\nf(4)=.a_41 a_42 a_43 a_44 ...\n.........\n.........\n\nSo each a_ij is an integer between 0 and 9. There is a slight ambiguity because of the non-uniqueness of decimal expansions. For such cases, we use the expansion with infinitely many 0's, so\n.25000000...\nrather than\n.2499999.....\n\nNow construct a new real number between 0 and 1 as follows:\nLet b_1 be different from a_11 and either 3 or 7.\nLet b_2 be different from a_22 and either 3 or 7.\nLet b_3 be different from a_33 and either 3 or 7.\n.....\nand let\nx=.b_1 b_2 b_3 b_4 .....\nThen x is in (0,1). But by construction, b is not equal to f(1) (since the first decimal digits are different). It is different from f(2) since the second decimal digit is different. Continue and see that x is not f(n) for *any* natural number n. In other words, x is not in the image of the function f!\n\nSince countability requires a function which is both one-to-one and onto, and we have shown that no function from N to (0,1) can be onto, we see that (0,1) is uncountable. Since R is even larger, R is uncountable.\n\nNote: I used the choice of 3 or 7 to make sure to avoid the ambiguity of decmal expansions.
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Try this link and read it all the way through.  It's short.\n\nhttp://mathcentral.uregina.ca/qq/database/QQ.09.00/tom3.html\n\nThis link is better:\n\nhttp://mathforum.org/library/drmath/view/56760.html\n\nJust scroll down.
978661
Have fun:\nhttp://www.math.nyu.edu/~griffith/teaching/06numanalysis/labs/bisection/
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The Edifier has it right, but darned if I can follow the notation. You really need to see this written out like a textbook to understand what's going on.\n\nClick the link below in "sources" to see the answer hosted at my website www.calculus-help.com. Right now, Yahoo! answers, as far as I can tell, doesn't allow graphics, which makes it tricky to answer ANY math questions.\n\nPlease don't post math answers, guys, if the poster knows the answer but can't get there, and you get something completely different.
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You should define your terms:\nWhat is µ?\nWhat is ¹s?\n\nAssuming µ is the angle the plane makes with the horizontal (traditionally this is Θ), and assuming ¹s is the coefficient of static friction between the block and the plane (traditionally, this is µ):\n\nI - T\nII - F\nIII - F\nIV - F\nV - F \nVI - T\n\nAnswer choice (2) satisfies these requirements.\n\nI always hated these types of questions.  They test your bookkeeping skills moreso than your knowledge of physics.  A simple T/F quiz is always better.
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You might find this paper useful\nhttp://arxiv.org/abs/math-ph/0106027
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http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
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Check out Stewart's Calculus(refer to the first link). If you are looking for something  more rigorous refer to Apostol's Calculus(refer to second link).
925132
TimGNO is correct, although a pedant would point out that he hasn't shown this point is a maximum.  But  it is common sense.  See my response to the second time you asked the question, I got the same answer (foolishly mucking around with tangents), but make a couple of other observations you may wish to look at.
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Way to go Arbitrage!  Oh to funny guy- yeah we get that E=MC2  IS a formula- but if you really want to "get it" Check out Maxwells equations. It's a great time to be a science nerd with all this info pouring in now! Figure it out & go up one on Albert!
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It is linear on intervals, on (- infinite, 0) and on (0, +infinite) but not on the whole R. \n\nTry plotting it, you get a reversed V, not a straight line.
1136350
Good Question, Mandelbrot's book and Barnsley's book will provide you with many examples.
737727
What does C represent?  If C is a constant, then this doesn't converge.\nWhat is the context?  What is the name of the class, chapter and section that this comes from?