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In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [ 1 ] As an example, " is less than " is a relation on the set of natural numbers; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3), and likewise between 3 and 4 (denoted as 3 < 4), but not between the ...
In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Every partial order and every equivalence relation is transitive. For example, less than and equality among real numbers are both transitive: If a < b and b < c then a < c; and if x ...
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
Binary relations, and especially homogeneous relations, are used in many branches of mathematics to model a wide variety of concepts. These include, among others: the "is greater than", "is equal to", and "divides" relations in arithmetic; the "is congruent to" relation in geometry; the "is adjacent to" relation in graph theory;
In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product X × X. [ 1 ] [ 2 ] [ 3 ] This is commonly phrased as "a relation on X " [ 4 ] or "a (binary) relation over X ".
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by ...
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R; S from two given binary relations R and S. In the calculus of relations, the composition of relations is called relative multiplication, [1] and its result is called a relative product. [2]: 40 Function composition is the special case ...
Definition of congruence in analytic geometry. In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the ...