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Diagonal intersection information


Diagonal intersection is a term used in mathematics, especially in set theory.

If is an ordinal number and is a sequence of subsets of , then the diagonal intersection, denoted by

is defined to be

That is, an ordinal is in the diagonal intersection if and only if it is contained in the first members of the sequence. This is the same as

where the closed interval from 0 to is used to avoid restricting the range of the intersection.

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Diagonal intersection

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Diagonal intersection is a term used in mathematics, especially in set theory. If δ {\displaystyle \displaystyle \delta } is an ordinal number and ⟨ X...

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Diagonal

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If no three diagonals of a convex polygon are concurrent at a point in the interior, the number of interior intersections of diagonals is given by (...

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Pedestrian scramble

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traffic, thereby allowing pedestrians to cross an intersection in every direction, including diagonally, at the same time. In Canada and the United States...

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Orthodiagonal quadrilateral

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parallel to the diagonals of ABCD. There are several metric characterizations regarding the four triangles formed by the diagonal intersection P and the vertices...

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Club filter

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} is a κ {\displaystyle \kappa } -complete filter closed under diagonal intersection called the club filter. To see that this is a filter, note that...

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Cyclic quadrilateral

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quadrilateral ABCD to be cyclic are: let E be the point of intersection of the diagonals, let F be the intersection point of the extensions of the sides AD and BC...

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Glossary of set theory

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Greek letter Δ) 1.  The symmetric difference of two sets 2.  A diagonal intersection ◊ The diamond principle ♣ A clubsuit principle □ The square principle...

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Diamond principle

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equivalent to a property of partitions of κ {\displaystyle \kappa } with diagonal intersection of initial segments of the partitions stationary in κ {\displaystyle...

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Club set

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\,} is a regular cardinal then club sets are also closed under diagonal intersection. In fact, if κ {\displaystyle \kappa \,} is regular and F {\displaystyle...

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Quadrilateral

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quadrilateral ABCD in which E is the point of intersection of the diagonals and F is the point of intersection of the extensions of sides BC and AD, let ω...

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Ineffable cardinal

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{\displaystyle \kappa } , there is a normal (i.e. closed under diagonal intersection) non-trivial κ {\displaystyle \kappa } -complete filter F {\displaystyle...

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Tangential quadrilateral

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the segments that the diagonal intersection P divides diagonal AC into as AP = p1 and PC = p2, and similarly P divides diagonal BD into segments BP =...

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Ramsey cardinal

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M-ultrafilter: for any sequence ⟨Xᵦ : β < κ⟩ ∈ M of members of U, the diagonal intersection ΔXᵦ = {α < κ : ∀β < α(α ∈ Xᵦ)} ∈ U, U is weakly amenable: for any...

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Diagonal method

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The diagonal method (DM) is a rule of thumb in photography, painting and drawing. Dutch photographer and lecturer Edwin Westhoff discovered the method...

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Marching tetrahedra

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edges: the original twelve, six face diagonals, and the main diagonal. Just like in marching cubes, the intersections of these edges with the isosurface...

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Touchscreen

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I/Os create a maximum of 64 sensing element intersections, whereas 16 diagonal I/Os create 120 intersections. 2015 BISTATE PROJECTED CAPACITANCE - When...

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Hindu temple architecture

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The second design of 4 padas has a symbolic central core at the diagonal intersection, and is also a meditative layout. The 9 pada design has a sacred...

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Brahmagupta theorem

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(that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side...

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Roundabout

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are all, with certain distinctions between them, a type of circular intersection or junction in which road traffic is permitted to flow in one direction...

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Mahlo cardinal

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and only if there is a normal (i.e. nontrivial and closed under diagonal intersections) κ-complete filter on the power set of κ that is closed under the...

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Bisection

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(that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side...

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Normal measure

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equivalent, the ultrafilter (set of sets of measure 1) is closed under diagonal intersection. For a normal measure, any closed unbounded (club) subset of κ contains...

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Optic equation

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sides as a and b and half the length of the segment through the diagonal intersection as c, the sum of the reciprocals of a and b equals the reciprocal...

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Overlapping circles grid

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circles intersecting at a point, with a 7th circle centered on that intersection. Overlapping circles with similar geometrical constructions have been...

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Parallelogram

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B and C (B ≠ C) and angle γ {\displaystyle \gamma } at the intersection of the diagonals is given by K = | tan ⁡ γ | 2 ⋅ | B 2 − C 2 | . {\displaystyle...

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