What is Chebychev’s Theorem?
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Do you mean Chebychev's theorem of proof of Bertrand's postulate on prime number distributions, or Chebychev's theorem concerning standard deviations? \n\nEdit your question to clarify and I'll answer more...\n\nOk, Chebychev's theorem states that at least 1-(1/k^2) of a distribution lies within k standard deviations of the mean.  The reason k must be more than 1 is that at that low of a standard deviation exactly what type of distribution you have becomes important.  Chebychev's theorem works for any distribution, so it can be used to assess general population size, at least within a fairly wide range, with less analysis using just the sample standard deviation.  So, it works for sparse data, non-normal distributions, and so on, within its limits of only holding for calculations of what lies within a range larger than one standard deviation.  \n\nSo, for example, you can take a small subset from a set of data with a mean of 50, and a *sample* standard deviation  of 8, and from Chebychev's theorem know that if you were to take a larger sample, at least 75% (1-1/2^2) would lie within the range of 44 to 66, that is, 50+/-16.
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Its the Pythagorean Theorem. It applies to right angle triangles. \nIt states that a^2 + b^2 = c^2\nWhere a and b represent the lengths of legs of the triangle and c is the Hypotenuse.\nThe Hypotenuse is the side that is opposite the right angle (also the longest side). Whereas the legs are the two sides that meet at the right angle.
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That is the central limit theorem.  Each distribution can be uniform, but the distributions themselves are normally distributed in their range, their value, their frequency.\nRead the attached link for more details.
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boy we carry those text books along with us\nif u want us to prove then provide the theorem plz
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Hint: Let C=X&#92;O and let f(x)=dist(x,C). The other way is trivial.
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You might try reading Whitehead and Russell's Principia Mathematica.  I can't promise it will help, as I haven't read it, but I've been told that this issue is addressed.
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Assume there is a pair a_i, b_j with a non zero product.\nWrite fg= (a_i x^i + other terms) (b_j x^j + other terms) =\na_i b_j x^(i+j) is non zero.\n\nContradiction.
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You might find this paper useful\nhttp://arxiv.org/abs/math-ph/0106027
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Try here (the content is very techinical).  http://scienceworld.wolfram.com/physics/ContinuityEquation.html\nhttp://www.efm.leeds.ac.uk/CIVE/CIVE1400/Section3/continuity.htm
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Reflection and refraction do not directly prove Huygen's Theorem, at least not in any way I'm familiar with. Diffraction patterns, such as those of single and double slits, are clear examples of Huygen's Theroem in action.\n(We haven't done wave optics yet)
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This is an inevitable occurrence; there is actually a theorem by Paul Erdos (I forget who he was working with) that is applicable...  Erdos-Schekeres Theorem, perhaps.  It's the one where they proved that if you take a piece of paper, cover the bottom of a box with it, remove it, wad it up and throw it back into the box, at least one point will be exactly above the same place it was before...  It doesn't take a whole lot of imagination to see a definite isomorphism between the E-S theorem (or whichever one it is) and what you're talking about.\n\nANYHOW, what it boils down to, in your case, is that you will have an experience (whether in dream or in reality is not germain) and it will match a future one.  On the whole, you should expect that to happen once in a while--and if you have a wide enough breadth of experience, perhaps more often...\n\nI'm not sure that this addresses your question.  If it doesn't, here's a shorter answer: It is part of normal life; it isn't a problem; and we all share it to some degree or other.
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the Chebyshev's inequality goes Pr(|X-mean| > or = k.sd)< or = 1/k^2\n\ni m assuming u meant standard deviation when u said 4.3818, which is 2 sd.\n\nThe prob of points outside 2sd at both sides is not more than 1/k^2.. or 1/2^2=1/4.\n\nSo, the probability of points within 2sd will be at least 1-1/4=3/4.\n\nhow many data points? if u have 100 data points in total, there will be at least 100x3/4=75 data points within the mean+/-4.3818 range.\n\nNote: The exactly probability depends on the type of distribution the data follows, for example, for Normal/Gaussian, 95% lies within +/- 1.96sd. Chebyshev's inequality states the minimum possible for any type of distribution.
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a^2 + b^2 = c^2\n\nPythagorean theorem
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By the transitive property, a=c
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http://en.wikipedia.org/wiki/Liskov_substitution_principle click the link to know in detail.
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Any on Analytic Geometry. My suggestion is "Analytic Geometry" by Charles Lehmann or "Modern Analytic Geometry" by William Wooton.
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Suppose f : D → R has a limit at x0. Prove that | f | : D → R has a limit at x0 and that limx→x0 | f(x) | = | limx→x0 f(x) |.\n\n\nLet limx→x0 f(x) = c\n\nNow | f(x) | = f(x) for f(x) ≥ 0 = c\n= -f(x) for f(x) < 0 = -c\n\nSo limx→x0 | f(x) |  \n\n= limx→x0 f(x) for f(x) ≥ 0 = c\nlimx→x0 -f(x) for f(x) <0 = - limx→x0 f(x) x < 0 = -c\n\n= |c|\n\n= | limx→x0 f(x) | .................... QED