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Floor function. Ceiling function. In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor (x). Similarly, the ceiling function maps x to the smallest integer greater than or equal to x, denoted ⌈x⌉ or ceil (x).
Greater-than sign. The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. [1] In mathematical writing, the greater-than sign is typically placed between ...
A minimal element of a subset of some preordered set is defined dually as an element of that is not greater than any other element in . The notions of maximal and minimal elements are weaker than those of greatest element and least element which are also known, respectively, as maximum and minimum. The maximum of a subset of a preordered set is ...
Upper and lower bounds. A set with upper bounds and its least upper bound. In mathematics, particularly in order theory, an upper bound or majorant [1] of a subset S of some preordered set (K, ≤) is an element of K that is greater than or equal to every element of S. [2] [3] Dually, a lower bound or minorant of S is defined to be an element ...
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
Infimum and supremum. A set of real numbers (hollow and filled circles), a subset of (filled circles), and the infimum of Note that for totally ordered finite sets, the infimum and the minimum are equal. A set of real numbers (blue circles), a set of upper bounds of (red diamond and circles), and the smallest such upper bound, that is, the ...
Less-than sign. The less-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the left, <, has been found in documents dated as far back as the 1560s. In mathematical writing, the less-than sign is typically placed between two values ...
The red subset = {,,,,,} has one greatest element, viz. 30, and one least element, viz. 1. These elements are also maximal and minimal elements , respectively, of the red subset. In mathematics , especially in order theory , the greatest element of a subset S {\displaystyle S} of a partially ordered set (poset) is an element of S {\displaystyle ...