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The Cauchy-Schwarz inequality
https://www.dpmms.cam.ac.uk/~wtg10/csineq.html4 Oct 2001: 1. /b. 1. rather than some other a. i. /b. i. , ... i. are equal. This still leaves a minor problem that some of the b. -
The fundamental theorem of arithmetic not always true.
https://www.dpmms.cam.ac.uk/~wtg10/meta.fta.html11 May 2001: If, however, I can construct some other mathematical object (the model) with those properties for which the theorem is false, then it is clear that my proof cannot work. ... However, in any context in which the lemma applies there has to be some notion -
Galois Theory Dr P.M.H. Wilson1 Michaelmas Term 2000 1LATEXed ...
https://www.dpmms.cam.ac.uk/study/II/Galois/Galois.pdf24 Oct 2001: If α B, then α A for some (A, θ) C,and so we let ψ(α) = θ(α). ... 1 2, 3. Suppose now that K = LG for some finite group G. -
The Cassels-Tate Pairing and thePlatonic Solids Tom FisherDepartment…
https://www.dpmms.cam.ac.uk/~taf1000/papers/ctp.pdf12 Oct 2001: We discuss descent bym-isogeny for some elliptic curves parametrised by X1(m) and X(m). ... im δm = Hom(Gv,〈rP sQ〉) (34). for some (r : s) P1(Z/mZ). -
The existence of root two
https://www.dpmms.cam.ac.uk/~wtg10/roottwo.html20 Sep 2001: We know that some numbers are irrational, but we can still describe them, by means of their decimal expansions. ... 2. in some way, consistent with the principle that 0 < a < b implies that a. -
Definitions
https://www.dpmms.cam.ac.uk/~wtg10/definition.html24 Nov 2001: In the end, in order to do this one is forced to come up with some non-canonical construction that satisfies the axiom. ... four times, being periodic with period some number (defined to be 2 pi), satisfying the addition law -
The mean value theorem
https://www.dpmms.cam.ac.uk/~wtg10/meanvalue.html13 Dec 2001: Then there is some point c in (a,b) such that f'(c) equals (f(b)-f(a))/(b-a). ... Here, I take f to be real valued and defined on some interval of real numbers.
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