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  2. Transitive relation - Wikipedia

    en.wikipedia.org/wiki/Transitive_relation

    The examples "is greater than", "is at least as great as", and "is equal to" are transitive relations on various sets. As are the set of real numbers or the set of natural numbers: whenever x > y and y > z, then also x > z whenever x ≥ y and y ≥ z, then also x ≥ z whenever x = y and y = z, then also x = z. More examples of transitive ...

  3. Sigmoid function - Wikipedia

    en.wikipedia.org/wiki/Sigmoid_function

    Here, is a free parameter encoding the slope at =, which must be greater than or equal to because any smaller value will result in a function with multiple inflection points, which is therefore not a true sigmoid.

  4. Relation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Relation_(mathematics)

    Greater than; Greater than or equal to; Less than; Less than or equal to; Divides (evenly) Subset of; Equivalence relations: Equality; Parallel with (for affine spaces) Is in bijection with; Isomorphic; Tolerance relation, a reflexive and symmetric relation: Dependency relation, a finite tolerance relation; Independency relation, the complement ...

  5. Transitive closure - Wikipedia

    en.wikipedia.org/wiki/Transitive_closure

    Examples of transitive relations include the equality relation on any set, the "less than or equal" relation on any linearly ordered set, and the relation "x was born before y" on the set of all people. Symbolically, this can be denoted as: if x < y and y < z then x < z. One example of a non-transitive relation is "city x can be reached via a ...

  6. Negative relationship - Wikipedia

    en.wikipedia.org/wiki/Negative_relationship

    A negative correlation between variables is also called inverse correlation. Negative correlation can be seen geometrically when two normalized random vectors are viewed as points on a sphere, and the correlation between them is the cosine of the circular arc of separation of the points on a great circle of the sphere. [ 1 ]

  7. Inequality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inequality_(mathematics)

    The relation not greater than can also be represented by , the symbol for "greater than" bisected by a slash, "not". The same is true for not less than , a ≮ b . {\displaystyle a\nless b.} The notation a ≠ b means that a is not equal to b ; this inequation sometimes is considered a form of strict inequality. [ 4 ]

  8. Equivalence relation - Wikipedia

    en.wikipedia.org/wiki/Equivalence_relation

    The relation "has a common factor greater than 1 with" between natural numbers greater than 1, is reflexive and symmetric, but not transitive. For example, the natural numbers 2 and 6 have a common factor greater than 1, and 6 and 3 have a common factor greater than 1, but 2 and 3 do not have a common factor greater than 1.

  9. Inverse function - Wikipedia

    en.wikipedia.org/wiki/Inverse_function

    The square root of x is a partial inverse to f(x) = x 2. Even if a function f is not one-to-one, it may be possible to define a partial inverse of f by restricting the domain. For example, the function = is not one-to-one, since x 2 = (−x) 2.