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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
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
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
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)
Cultural region in France
least 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
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
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
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 inside the circle from upper-left to lower-right. It is typically
No_symbol
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
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
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)
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)
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
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
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
Four-sided polygon
the diagonals cross at right angles. Equidiagonal quadrilateral: the diagonals are of equal length. Bisect-diagonal quadrilateral: one diagonal bisects
Quadrilateral
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
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)
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
French geographer
Gravier (J. - F.). Paris and the French desert in 1972, Flammarion, Paris, 1972, 284 p. Empty diagonal Regional planning Decentralization v t e v t e
Jean-François_Gravier
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
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
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)
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 and a 2-tuple are commonly called a singleton and an ordered
Tuple
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
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
Set of elements common to all of some sets
{\displaystyle A\cap B=B\cap A.} The intersection of any set with the empty set results in the empty set; that is, that for any set A {\displaystyle A} , A ∩ ∅ =
Intersection_(set_theory)
Mathematical set formed from two given sets
}&X_{n}\\X_{1}&X_{2}&\dots &X_{n-1}&A_{n}^{\complement }\end{array}}\right]} . The diagonal components of this matrix A i ∁ {\displaystyle A_{i}^{\complement }} are
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
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
Board game
considered to be the parent of draughts (US: checkers) and Fanorona and the diagonals of its grid are the predecessor of the checkering of the draughts board
Alquerque
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
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
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
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
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
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
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
Set of elements in any of some sets
zero ( 0 {\displaystyle 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
jumps made by a single piece; the jumps do not need to be on the same diagonal direction and may "zigzag" (change direction). In American checkers and
Checkers
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
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
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
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
Square matrix used to represent a graph or network
graph contains all ones except along the diagonal where there are only zeros. The adjacency matrix of an empty graph is a zero matrix. The adjacency matrix
Adjacency_matrix
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
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. The modern
Reversi
Large board variant of shogi
left and backward right diagonals, and one square along the horizontal, the forward right diagonal, and the backward left diagonal (giving symmetry with
Dai_dai_shogi
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
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
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
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
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
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
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)
Collection of mathematical objects
0 {\displaystyle \aleph _{0}} are called uncountable sets. Cantor's diagonal argument shows that, for every set S {\displaystyle S} , its power set
Set_(mathematics)
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
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
This section is empty. You can help by adding to it. (July 2010)
List_of_highways_in_Brazil
Recursive integer sequence
be the number of vertical edges above the diagonal. For example, in Figure 2, the edges above the diagonal are marked in red, so the exceedance of this
Catalan_number
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
Standard system of axiomatic set theory
and the axiom of the empty set. On the other hand, the axiom schema of specification can be used to prove the existence of the empty set, denoted ∅ {\displaystyle
Zermelo–Fraenkel_set_theory
Mathematical use of "there exists"
\varnothing } 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
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
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
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
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
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)
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
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
Symbol representing a mathematical concept
object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra). Theories with a non-empty set of equations
Function_symbol
Finite sets whose elements are all hereditarily finite sets
the way down to the empty set. A recursive definition of well-founded hereditarily finite sets is as follows: Base case: The empty set is a hereditarily
Hereditarily_finite_set
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
Theoretical electronic band structure model in which the potential is periodic and weak
The empty lattice approximation is a theoretical electronic band structure model in which the potential is periodic and weak (close to constant). One
Empty_lattice_approximation
Set with exactly one element
{\displaystyle \{1\}} are not the same thing, and the empty set is distinct from the set containing only the empty set. A set such as { { 1 , 2 , 3 } } {\displaystyle
Singleton_(mathematics)
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
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
Naval artillery piece
The newer "Super Rapid" version with a diagonal, stealthy turret
OTO_Melara_76_mm
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
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
Topics referred to by the same term
interval, an interval of distance 1 Unit matrix, a diagonal matrix such that all elements on the main diagonal are 1 and all the others are zero Unit round-off
Unit
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
Axiom of set theory
foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic
Axiom_of_regularity
Assignment of meaning to the symbols of a formal language
fails in any structure with an empty domain. Thus the proof theory of first-order logic becomes more complicated when empty structures are permitted. However
Interpretation_(logic)
Board game
player wins by getting five of their marbles in a vertical, horizontal, or diagonal row (either before or after the sub-board rotation in their move). If all
Pentago
Mathematical use of "for all"
\exists _{!}S=\exists x.S(x),} which is true if S {\displaystyle S} is not empty, and ∀ ! S = ∀ x . S ( x ) , {\displaystyle \forall _{!}S=\forall x.S(x)
Universal_quantification
Board game variant from Tanzania
light (or empty) square. Either player may move first, by mutual agreement. The following rules apply to gameplay: Men move forward diagonally, one square
Tanzanian_draughts
Set whose elements all belong to another set
strict) superset of A, denoted by B ⊋ A . {\displaystyle B\supsetneq A.} The empty set, written { } {\displaystyle \{\}} or ∅ , {\displaystyle \varnothing
Subset
Game native to Myanmar
rows and 8 columns, without alternating colors. The board has also two diagonal lines from corner to corner, which are known as sit-ke-myin (Burmese: စစ်ကဲမျဉ်း
Sittuyin
Board game
without taking, one square diagonally forward, but take by jumping two squares diagonally forward over an enemy piece to an empty square, thereby removing
Cheskers
Set theory concept
as follows. (An empty box represents the empty set. A box containing only an empty box represents the set containing only the empty set, and so forth
Von_Neumann_universe
Playing piece with non-standard chess rules
moves to the corresponding diagonal moves, (e.g. W ⟷ F) and vice versa. (So mafsW is the xiangqi horse, move to an empty W-square, and continue one F-step
Fairy_chess_piece
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
Size of a set in mathematics
} , including the empty set and N {\displaystyle \mathbb {N} } itself. The method is much closer to Cantor's original diagonal argument. Again, assume
Cardinality
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
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
EMPTY DIAGONAL
EMPTY DIAGONAL
Boy/Male
Biblical
Who is empty or exhausted.
Girl/Female
Biblical
Empty, temple of the head.
Boy/Male
Hindu, Indian
Empty
Girl/Female
Biblical
Den, cave, making empty.
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).
Girl/Female
Biblical
Den, making empty, watching.
Biblical
den; cave; making empty
Boy/Male
Tamil
One who is empty, Hollow, Vain
Girl/Female
Biblical
Void, empty.
Biblical
empty; temple of the head
Biblical
den; making empty; watching
Boy/Male
Arabic
Empty.
Boy/Male
Hindu
One who is empty, Hollow, Vain
Biblical
who is empty, exhausted;free, empty, exhausted;
Boy/Male
British, English, Spanish
Strong Leader; Empty
Boy/Male
American, Australian, Danish, French, Jamaican, Latin
Vain; Empty; Poor; Robbed; Hollow
Boy/Male
Arabic, Australian, German, Greek, Kurdish
Empty; Void
EMPTY DIAGONAL
EMPTY DIAGONAL
Boy/Male
Arabic, Muslim
Praised by the Prophet
Boy/Male
Buddhist, Indian
Great Light
Boy/Male
Hindu, Indian
A River
Boy/Male
Tamil
Shrinay | à®·à¯à®°à¯€à®¨à®¾à®¯
Girl/Female
Russian
Holy.
Girl/Female
Arabic, Muslim
One who Controls or Suppresses her Anger; Feminine of Kazim
Girl/Female
American, Christian, German, Swedish
Noble Kind; Kind Spirit; Brightness; Form of Adelaide
Boy/Male
Hindu
Angel of God on earth, King of the earth
Boy/Male
Hindu
First Ray of sunlight
Boy/Male
Indian, Punjabi, Sikh
True Knowledge
EMPTY DIAGONAL
EMPTY DIAGONAL
EMPTY DIAGONAL
EMPTY DIAGONAL
EMPTY DIAGONAL
compar.
of Empty.
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.
a.
Empty.
p. pr. & vb. n.
of Empty
superl.
Destitute of reality, or real existence; unsubstantial; as, empty dreams.
a.
To empty.
a.
Empty; frivolous.
a.
Empty.
v. i.
To become empty.
v. t.
To empty.
pl.
of Empty
v. t.
To empty.
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.
n.
Love of empty of empty talk or noise.
superl.
Destitute of effect, sincerity, or sense; -- said of language; as, empty words, or threats.
superl.
Producing nothing; unfruitful; -- said of a plant or tree; as, an empty vine.
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, or lacking, sense, knowledge, or courtesy; as, empty brains; an empty coxcomb.
v. t.
To empty.