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Band of low-density population in France
The empty diagonal (French: diagonale du vide) is a band of low-density population that stretches from the French department of the Landes in the southwest
Empty_diagonal
Proof in set theory
Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence
Cantor's_diagonal_argument
Economically depressed area of rural Denmark
a term for a region in the United States marked by economic decline Empty Diagonal – a low-density population region in France Golden Banana Blue Banana
Rotten_Banana
Mathematical set containing no elements
In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic
Empty_set
Department of France
of its low population density Meuse is considered to fall within the empty diagonal. The most populous commune is Verdun; the prefecture, Bar-le-Duc, is
Meuse_(department)
High population and GDP corridor in Europe
Demographics of Europe Four Motors for Europe Golden Banana French Empty diagonal List of metropolitan areas in the European Union by GDP Northeast megalopolis
Blue_Banana
Cultural region in France
populated regions in southern Europe, and lies at the heart of the empty diagonal, a swath of sparsely populated territory running from northeastern to
Auvergne
Administrative subdivision in France
departments (2007). The broken lines mark the approximate boundaries of the empty diagonal. The solid line is the Le Havre-Marseille line, to the east of which
Departments_of_France
Department of France in Occitanie
of its low population density, it is considered to fall within the empty diagonal. The department also has the lowest urbanization rate in France, with
Lozère
Concept in human demographics
emigration, due to natural disasters and economic difficulties. The term 'Empty diagonal' is used for French departments that have low or declining populations
Population_decline
Department in Auvergne-Rhône-Alpes, France
of its low population density, it is considered to fall within the empty diagonal. Since the early 1980s Allier has faced many demographic handicaps.
Allier
European inhabitants of New Caledonia
well as settlers from the poorest regions of France in what is now the empty diagonal. However, as previously mentioned, there were also a large number of
Caldoche
Children forcibly moved from Réunion to France 1963–1982)
Réunion, in order to repopulate metropolitan departments mostly in the empty diagonal such as Creuse, Tarn, Gers, Lozère and East Pyrenees which had lost
Children_of_Creuse
Department in Auvergne-Rhône-Alpes, France
department falls within the band of low-density population known as the empty diagonal. Population development since 1791: The department counts several remarkable
Cantal
Array of numbers
matrices and D is a diagonal matrix. The eigendecomposition or diagonalization expresses A as a product VDV−1, where D is a diagonal matrix and V is a suitable
Matrix_(mathematics)
Term referring to the culture of French provincial towns and village life
Nièvre, a rural department in the empty diagonal, is a prime example of France profonde. It first returned François Mitterrand to the National Assembly
France_profonde
Mixed use development in Saint Paul, Minnesota, US
have run from downtown Saint Paul to the Minnesota State Capitol. An empty diagonal slat between the Bremer Tower and UBS Plaza towers marks where the terminal
Town_Square_(Saint_Paul)
Red circle with a red diagonal line, indicating something is not permitted
interdictory circle, and the prohibited symbol, is a red circle with a 45-degree diagonal line from upper left to lower right inside the circle. It is typically
No_symbol
Limitative results in mathematical logic
shows that no such system can demonstrate its own consistency. Employing a diagonal argument, Gödel's incompleteness theorems were among the first of several
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Set of elements common to all of some sets
and B, one hasA∩B=B∩A. The intersection of any set with the empty set results in the empty set; that is, that for any set A, A∩∅=∅ Also, the intersection
Intersection_(set_theory)
Finite ordered list of elements
where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple, a 2-tuple, and a 3-tuple are commonly called respectively
Tuple
French geographer
réédition numérique. ISBN 978-2-402-19129-6. {{cite book}}: ISBN / Date incompatibility (help) Empty diagonal Regional planning Decentralization v t e v t e
Jean-François_Gravier
can move forwards, straight ahead or diagonally, or sideways to an orthogonally adjacent field if that field is empty. Kings may move in all directions (up
Armenian_draughts
Photography
The diagonal method (DM) is a rule of thumb in photography, painting, and drawing. Dutch photographer and lecturer Edwin Westhoff discovered the method
Diagonal_method
Four-sided polygon
the diagonals cross at right angles. Equidiagonal quadrilateral: the diagonals are of equal length. Bisect-diagonal quadrilateral: one diagonal bisects
Quadrilateral
given a morphism of schemes p : X → S {\displaystyle p:X\to S} , the diagonal morphism δ : X → X × S X {\displaystyle \delta :X\to X\times _{S}X} is
Diagonal morphism (algebraic geometry)
Diagonal_morphism_(algebraic_geometry)
Special kind of square matrix
entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero. Because
Triangular_matrix
The Korean martial art Taekwondo has several stances used for different activities. These stances are most commonly seen in the form competition of Hyeong
Taekwondo_stances
Every set is smaller than its power set
subset is given by the following construction, sometimes called the Cantor diagonal set of f {\displaystyle f} : B = { x ∈ A ∣ x ∉ f ( x ) } . {\displaystyle
Cantor's_theorem
Mathematical puzzle
on a Cartesian grid with diagonal lines of slope −1 (such that x + y = c o n s t . {\displaystyle x+y=const.} on these diagonal lines, which represent pouring
Water_pouring_puzzle
Topics referred to by the same term
Scandinavian vowel letter. The letter Ø or the symbol ∅ (a circle crossed by a diagonal slash) etc. may also refer to: Close-mid front rounded vowel (IPA: ø) Zero
Ø_(disambiguation)
Mathematical set formed from two given sets
2⋯An−1∁XnX1X2⋯Xn−1An∁]. The diagonal components of this matrix Ai∁ are equal correspondingly to Xi∖Ai. In NTA, a diagonal C-system A∁, that represents
Cartesian_product
Probability saying
almost surely not land on a diagonal), even though the set of points on the diagonals is not empty, and a point on a diagonal is no less possible than any
Almost_surely
Paper-and-pencil game for two players
Os. A player wins when they mark all three spaces of a row, column, or diagonal of the grid, whereupon they traditionally draw a line through those three
Tic-tac-toe
Shape in the game of Go
game of Go, the empty triangle is the most fundamental example of the concept of bad shape. Three stones of one color form an empty triangle when they
Empty_triangle
Sequence of words formed by specific rules
composed of. For any alphabet, there is only one word of length 0, the empty word, which is often denoted by e, ε, λ or even Λ. By concatenation one
Formal_language
Set of elements in any of some sets
refers to a union of zero (0) sets and it is by definition equal to the empty set. For explanation of the symbols used in this article, refer to the table
Union_(set_theory)
Strategy board game
same rules as Othello where the first four pieces go in the center in a diagonal pattern and the player who cannot make a move simply passes, rather than
Reversi
Mathematician (1845–1918)
and subsequently made further important contributions, including his diagonal argument and theorem. However, he never again attained the high level of
Georg_Cantor
Strategy board game
the beginning of the game. At the beginning of a player's turn, if the diagonal square of a player's piece (in the player's forward direction) contains
Checkers
In mathematics, invariant of square matrices
of scalars and whose value on a triangular matrix is the product of the diagonal entries. So, the determinant of the product of two square matrices is the
Determinant
Matrix in mathematics
deleting a set, possibly empty, of corresponding rows and columns of A is positive. A + D is non-singular for each nonnegative diagonal matrix D. Every real
M-matrix
Strategy board game
uses this board with a cross in the center. Twelve men's morris adds four diagonal lines to the board and gives each player twelve pieces. This means the
Nine_men's_morris
2D cellular automaton devised by Brian Silverman in 1987
one cell away (range value of one) in any direction, both orthogonal and diagonal. These simple rules can be used to construct logic gates (see below). Entities
Wireworld
Abstract strategy game
vertical lines and 2 diagonal lines. The board is empty to begin the game, and players take turns placing their pieces on empty intersections. Once all
Three_men's_morris
Mathematical operation in quantum optics, general relativity and other areas of physics
used to diagonalize Hamiltonians, with a corresponding transformation of the state function. Operator eigenvalues calculated with the diagonalized Hamiltonian
Bogoliubov_transformation
Topics referred to by the same term
disjoint union of a perfect set and a countable set Georg Cantor Cantor's diagonal argument This disambiguation page lists mathematics articles associated
Cantor's theorem (disambiguation)
Cantor's_theorem_(disambiguation)
Branch of mathematics that studies sets
uncountability proof, which differs from the more familiar proof using his diagonal argument. Cantor introduced fundamental constructions in set theory, such
Set_theory
Type of transposition cipher
y=2. Or, 6 rails, 5 diagonals (4+1), and 2 empty spaces at the end. By blocking out the empty spaces at the end of the last diagonal, we can simply fill
Rail_fence_cipher
Mathematical use of "there exists"
because ∅ denotes the empty set, and no x of any description – let alone an x fulfilling a given predicate P(x) – exist in the empty set. See also Vacuous
Existential_quantification
Class of algorithms
can traverse any (countably) infinite tree, essentially via a diagonal argument ("diagonal"—a combination of vertical and horizontal—corresponds to a combination
Tree_traversal
Collection of mathematical objects
cardinality strictly greater than ℵ0 are called uncountable sets. Cantor's diagonal argument shows that, for every set S, its power set (the set of its subsets)
Set_(mathematics)
Mathematical puzzle by John Conway
soldier jumping over an adjacent soldier into an empty cell, vertically or horizontally (but not diagonally), and removing the soldier which was jumped over
Conway's_Soldiers
Standard system of axiomatic set theory
of defining the semantics. The structure S=(𝔻,ℐ∈,μ) consists of a non-empty set 𝔻, called the domain of discourse, a relation ℐ∈⊆𝔻2, called the interpretation
Zermelo–Fraenkel_set_theory
Recursive integer sequence
the edges of a grid with n × n square cells, which do not pass above the diagonal. A monotonic path is one which starts in the lower left corner, finishes
Catalan_number
Abstract strategy board game
one space diagonally forward as shown. A hop consists of jumping over a single adjacent piece, either one's own or an opponent's, to the empty space directly
Chinese_checkers
Multiple equivalent ways to define a topological space
then x ∙ {\displaystyle x_{\bullet }} converges to x . {\displaystyle x.} Diagonal principle/Convergence of iterated limits. If ( x a ) a ∈ A → x {\displaystyle
Axiomatic foundations of topological spaces
Axiomatic_foundations_of_topological_spaces
Informal set theories
completely by its elements, there can be only one empty set. (See axiom of empty set.) Although the empty set has no members, it can be a member of other
Naive_set_theory
Memorial in Christchurch, New Zealand
185 empty chairs, also known as 185 white chairs or 185 empty white chairs or simply as 185 chairs, was an unofficial memorial for the 185 individuals
185_empty_chairs
Size of a possibly infinite set
new cardinal number as it does for natural numbers. However, Cantor's diagonal argument shows that the power set operation always results in a strictly
Cardinal_number
Glyph variant of numeral 0 (zero) with slash
"short diagonal stroked form", on this browser it produces 0︀. Note that the above should not be confused with the "slashed zero variant of the empty set"
Slashed_zero
configurations of multiple hard drives not referred to by RAID acronyms. Row diagonal parity (RDP) is a scheme where one dedicated disk of parity is in a horizontal
Non-standard_RAID_levels
Paradox in set theory
formulated his own paradox, which relied on reasoning similar to Cantor's diagonal argument. According to Hilbert, it even initiated Ernst Zermelo's version
Russell's_paradox
Mathematical set of all subsets of a set
(or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed, for example, in
Power_set
Board game
Jump: A jump consists of moving a piece that is diagonally adjacent an opponent's piece, to an empty square immediately beyond it in the same direction
English_draughts
Skyscraper in Catalonia, Spain
(pronounced [ˈtorə əɡˈbaɾ]), is a 38-story skyscraper located between Avinguda Diagonal and Carrer Badajoz, near Plaça de les Glòries Catalanes, which marks the
Torre_Glòries
Elements in exactly one of two sets
an abelian group under the operation of symmetric difference, with the empty set as the neutral element of the group and every element in this group
Symmetric_difference
Pair of logical equivalences
Cardinal number (large) Class Constructible universe Continuum hypothesis Diagonal argument Element ordered pair tuple Family Forcing One-to-one correspondence
De_Morgan's_laws
On the number of united points of a correspondence from an algebraic curve to itself
diagonal of C×C. The Chasles–Cayley–Brill formula follows easily from this together with the fact that the self-intersection number of the diagonal is
Chasles–Cayley–Brill_formula
Two-player board game
objective of the game is to be the first to form a horizontal, vertical, or diagonal line of four of one's own tokens. It is therefore a type of m,n,k-game
Connect_Four
Generalization of "n-th" to infinite cases
numbers that include the natural numbers and have the property that every non-empty collection (set or proper class) of ordinals has a least or "smallest" element
Ordinal_number
Concept in axiomatic set theory
f(x) in the axiom schema of specification is the empty set, whose existence (i.e., the axiom of empty set) is then needed. For this reason, the axiom schema
Axiom_schema_of_specification
Square matrix used to represent a graph or network
adjacency matrix of an empty graph is a zero matrix. The adjacency matrix of a complete graph contains all ones except along the diagonal where there are only
Adjacency_matrix
Diagram in systems analysis
N2 chart is shown in Figure 2. The system functions are placed on the diagonal; the remainder of the squares in the N × N matrix represent the interface
N2_chart
Smallest rectangle which encloses some planar set of points
dataset consisting of a diagonal line, or a small number of disjunct points (patchy data), then most of the MBR will be empty and an "overlapping rectangles"
Minimum_bounding_rectangle
Diagonal intersection is a term used in mathematics, especially in set theory. If δ is an ordinal number and ⟨Xα∣α<δ⟩ is a sequence of subsets of δ, then
Diagonal_intersection
Commemorative coins of the Eurozone 2020-2029
indication of the issuing country 'FI', the mintmark and the year '2024' run diagonally between the buildings. The texts and the silhouettes of the buildings
List of 2 euro commemorative coins (2020–2029)
List_of_2_euro_commemorative_coins_(2020–2029)
Diagram that shows all possible logical relations between a collection of sets
zones in a given context. In Venn diagrams, a shaded zone may represent an empty zone, whereas in an Euler diagram, the corresponding zone is missing from
Venn_diagram
Computer graphics rendering algorithm
we now have nineteen edges: the original twelve, six face diagonals, and the main diagonal. Just like in marching cubes, the intersections of these edges
Marching_tetrahedra
Infinite cardinal number
Tarski's undefinability Banach–Tarski paradox Cantor's theorem – paradox – diagonal argument Compactness Halting problem Lindström's Löwenheim–Skolem Russell's
Aleph_number
Logic puzzle
empty. Another fairly common pattern is a 1 diagonally adjacent to a 2, with one of the spaces next to the 2 but not adjacent to the 1 either empty or
Light_Up_(puzzle)
Sliding puzzle with fifteen pieces and one space
permutations can be obtained. The exceptional graph is a regular hexagon with one diagonal and a vertex at the center added; only 1/6 of its permutations can be
15_puzzle
Board game variant from Tanzania
a light (or empty) square. Either player may move first, by mutual agreement. The following rules apply to gameplay: Men move diagonally forward by one
Tanzanian_draughts
Proof by Alan Turing
"diagonal process", in fact shows that his machine (called H) cannot calculate its own number, let alone the entire diagonal number (Cantor's diagonal
Turing's_proof
Board game
may be moved only to an empty space adjacent to its starting space, meaning adjacent horizontally, vertically, or diagonally, as indicated by the connecting
Teeko
or diagonally and is then the winner of the game. Mojo Too is similar in principle and played with 3 pieces and 1 pawn each. Starting with an empty board
Mojo_(board_game)
Mathematical set that can be enumerated
than the set of natural numbers and is said to be uncountable. Cantor's diagonal argument provides a formal proof by using a reductio ad absurdum strategy
Countable_set
Type of two player board game
one side of the board. The fox and geese can move to any empty space around them (also diagonally). The fox can jump over geese like in checkers, capturing
Fox_games
Wrong Diagonal Bishop ☖ pieces in hand: 角 ☗ pieces in hand: – Bishop Exchange Wrong Diagonal Bishop (角換わり筋違い角 kakugawari suji chigai kaku) is a variation
Bishop Exchange, Wrong Diagonal Bishop
Bishop_Exchange,_Wrong_Diagonal_Bishop
Maximal proper filter
filter. (In the above, by definition a filter on a set does not contain the empty set.) Equivalently, an ultrafilter on the set X can also be characterized
Ultrafilter_on_a_set
Korean abstract strategy board game
pieces. The players take turns moving one of their pieces one square diagonally. The first player to move all of their pieces to their opponent's starting
Five-field_kono
Identities and relationships involving sets
Two additional pairs of properties involve the special sets called the empty set ∅ and the universe set 𝑼. These sets have no members, and the universe
Algebra_of_sets
Abstract mathematics problem
his 1988 book A First Course in Probability. The problem starts with an empty vase and an infinite supply of balls. An infinite number of steps are then
Ross–Littlewood_paradox
Theorem extending pre-measures to measures
diagonal has measure 0. The measure of a subset is ∫01n(x)dx where n(x) is the number of points of the subset with given x-coordinate. The diagonal has
Carathéodory's extension theorem
Carathéodory's_extension_theorem
Measurable set whose measure is zero
be confused with the empty set as defined in set theory. Although the empty set has Lebesgue measure zero, there are also non-empty sets which are null
Null_set
Set whose elements all belong to another set
equivalently, B is a proper (or strict) superset of A, denoted by B⊋A. The empty set, written {} or ∅, has no elements, and therefore is vacuously a subset
Subset
Problem in geometry
few observations. For the number of regions to be maximized, no three diagonals should cross at the same point, for otherwise a small perturbation to
Moser's_circle_problem
Graphical aid for deriving some concepts in combinatorics
1)st diagonal of Pascal's triangle. For example, when k = 3 the nth number is the (n + 1)st triangular number, which falls on the second diagonal, 1, 3
Stars and bars (combinatorics)
Stars_and_bars_(combinatorics)
Axiom of set theory
Informally put, the axiom of choice says that given any collection of non-empty sets, one can identify another set containing one element chosen from each
Axiom_of_choice
25x25 grid variant of Japanese chess
right or rear left diagonals, or one square orthogonally or on the rear right diagonal. It has no move along the fore left diagonal. ([fr][bl]BW[br]F)
Tai_shogi
travel, tourism, insurance
EMPTY DIAGONAL
EMPTY DIAGONAL
Boy/Male
Arabic
Empty.
Biblical
who is empty, exhausted;free, empty, exhausted;
Boy/Male
Biblical
Who is empty or exhausted.
Boy/Male
American, Australian, Danish, French, Jamaican, Latin
Vain; Empty; Poor; Robbed; Hollow
Boy/Male
Arabic, Australian, German, Greek, Kurdish
Empty; Void
Biblical
den; cave; making empty
Biblical
den; making empty; watching
Girl/Female
Biblical
Den, making empty, watching.
Girl/Female
Biblical
Void, empty.
Boy/Male
Tamil
One who is empty, Hollow, Vain
Girl/Female
Biblical
Empty, temple of the head.
Surname or Lastname
English
English : nickname for a foolish or eccentric person, from a diminutive of Foll, from Old French fol ‘mad’, ‘stupid’ (Late Latin follis, originally a noun denoting any of various objects filled with air, but later transferred to vain and empty-headed notions).
Boy/Male
British, English, Spanish
Strong Leader; Empty
Boy/Male
Hindu
One who is empty, Hollow, Vain
Biblical
empty; temple of the head
Boy/Male
Hindu, Indian
Empty
Girl/Female
Biblical
Den, cave, making empty.
EMPTY DIAGONAL
EMPTY DIAGONAL
EMPTY DIAGONAL
EMPTY DIAGONAL
EMPTY DIAGONAL
EMPTY DIAGONAL
EMPTY DIAGONAL
a.
Empty.
superl.
Destitute of, or lacking, sense, knowledge, or courtesy; as, empty brains; an empty coxcomb.
p. pr. & vb. n.
of Empty
imp. & p. p.
of Empty
n.
An empty box, crate, cask, etc.; -- used in commerce, esp. in transportation of freight; as, "special rates for empties."
superl.
Destitute of effect, sincerity, or sense; -- said of language; as, empty words, or threats.
superl.
Destitute of reality, or real existence; unsubstantial; as, empty dreams.
superl.
Containing nothing; not holding or having anything within; void of contents or appropriate contents; not filled; -- said of an inclosure, as a box, room, house, etc.; as, an empty chest, room, purse, or pitcher; an empty stomach; empty shackles.
a.
Empty; frivolous.
n.
Love of empty of empty talk or noise.
v. t.
To empty.
superl.
Producing nothing; unfruitful; -- said of a plant or tree; as, an empty vine.
v. t.
To deprive of the contents; to exhaust; to make void or destitute; to make vacant; to pour out; to discharge; as, to empty a vessel; to empty a well or a cistern.
v. t.
To empty.
a.
Empty.
a.
To empty.
pl.
of Empty
compar.
of Empty.
v. i.
To become empty.
v. t.
To empty.
travel, tourism, insurance