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An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.
In logic, equality is a primitive predicate (a statement that may have free variables) with the reflexive property (called the Law of identity), and the substitution property. From those, one can derive the rest of the properties usually needed for equality.
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number is equal to itself (reflexive).
Reflective property of a parabola. The reflective property states that if a parabola can reflect light, then light that enters it travelling parallel to the axis of symmetry is reflected toward the focus. This is derived from geometrical optics, based on the assumption that light travels in rays. Consider the parabola y = x 2. Since all ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
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If equals are added to equals, then the wholes are equal (Addition property of equality). If equals are subtracted from equals, then the differences are equal (subtraction property of equality). Things that coincide with one another are equal to one another (reflexive property). The whole is greater than the part.
indicates that the column's property is always true for the row's term (at the very left), while indicates that the property is not guaranteed in general (it might, or might not, hold). For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by Y in the "Symmetric" column and in the ...