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  2. List of mathematical proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_proofs

    set is smaller than its power set; uncountability of the real numbers; Cantor's first uncountability proof. uncountability of the real numbers; Combinatorics; Combinatory logic; Co-NP; Coset; Countable. countability of a subset of a countable set (to do) Angle of parallelism; Galois group. Fundamental theorem of Galois theory (to do) Gödel number

  3. Resolvent set - Wikipedia

    en.wikipedia.org/wiki/Resolvent_set

    In linear algebra and operator theory, the resolvent set of a linear operator is a set of complex numbers for which the operator is in some sense "well-behaved". The resolvent set plays an important role in the resolvent formalism .

  4. Baker–Campbell–Hausdorff formula - Wikipedia

    en.wikipedia.org/wiki/Baker–Campbell...

    The following identity (Campbell 1897) leads to a special case of the Baker–Campbell–Hausdorff formula. Let G be a matrix Lie group and g its corresponding Lie algebra. Let ad X be the linear operator on g defined by ad X Y = [X,Y] = XY − YX for some fixed X ∈ g. (The adjoint endomorphism encountered above.)

  5. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    List of logarithmic identities; List of mathematical functions; List of mathematical identities; List of mathematical proofs; List of misnamed theorems; List of scientific laws; List of theories; Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.

  6. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    P. Oxy. 29, one of the oldest surviving fragments of Euclid's Elements, a textbook used for millennia to teach proof-writing techniques. The diagram accompanies Book II, Proposition 5. [1] A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the

  7. Hilbert's basis theorem - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_basis_theorem

    The theorem is interpreted in algebraic geometry as follows: every algebraic set is the set of the common zeros of finitely many polynomials. Hilbert's proof is highly non-constructive : it proceeds by induction on the number of variables, and, at each induction step uses the non-constructive proof for one variable less.

  8. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    To investigate the left distributivity of set subtraction over unions or intersections, consider how the sets involved in (both of) De Morgan's laws are all related: () = = () always holds (the equalities on the left and right are De Morgan's laws) but equality is not guaranteed in general (that is, the containment might be strict).

  9. Polarization identity - Wikipedia

    en.wikipedia.org/wiki/Polarization_identity

    In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. If a norm arises from an inner product then the polarization identity can be used to express this inner product entirely in terms of the norm. The ...

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