Solution (chemistry)In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together, the solvent particles pull the solute particles apart and surround them. These surrounded solute particles then move away from the solid solute and out into the solution.
Bounded functionIn mathematics, a function f defined on some set X with real or complex values is called bounded if the set of its values is bounded. In other words, there exists a real number M such that for all x in X. A function that is not bounded is said to be unbounded. If f is real-valued and f(x) ≤ A for all x in X, then the function is said to be bounded (from) above by A. If f(x) ≥ B for all x in X, then the function is said to be bounded (from) below by B. A real-valued function is bounded if and only if it is bounded from above and below.
Aqueous solutionAn aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be represented as . The word aqueous (which comes from aqua) means pertaining to, related to, similar to, or dissolved in, water. As water is an excellent solvent and is also naturally abundant, it is a ubiquitous solvent in chemistry.
Melting pointThe melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at a standard pressure such as 1 atmosphere or 100 kPa. When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point or crystallization point.
Accumulation pointIn mathematics, a limit point, accumulation point, or cluster point of a set in a topological space is a point that can be "approximated" by points of in the sense that every neighbourhood of with respect to the topology on also contains a point of other than itself. A limit point of a set does not itself have to be an element of There is also a closely related concept for sequences.
SystemA system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity.
Unique factorization domainIn mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial commutative ring in which the product of any two non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units.
Inverse elementIn mathematics, the concept of an inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers. Given an operation denoted here ∗, and an identity element denoted e, if x ∗ y = e, one says that x is a left inverse of y, and that y is a right inverse of x. (An identity element is an element such that x * e = x and e * y = y for all x and y for which the left-hand sides are defined.
Triple pointIn thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. It is that temperature and pressure at which the sublimation, fusion, and vaporisation curves meet. For example, the triple point of mercury occurs at a temperature of and a pressure of 0.165 mPa. In addition to the triple point for solid, liquid, and gas phases, a triple point may involve more than one solid phase, for substances with multiple polymorphs.
Inverse functionIn mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by For a function , its inverse admits an explicit description: it sends each element to the unique element such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result.
Point (geometry)In classical Euclidean geometry, a point is a primitive notion that models an exact location in space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space. Being a primitive notion means that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy; for example, "there is exactly one line that passes through two different points".
Inverse semigroupIn group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse y in S in the sense that x = xyx and y = yxy, i.e. a regular semigroup in which every element has a unique inverse. Inverse semigroups appear in a range of contexts; for example, they can be employed in the study of partial symmetries. (The convention followed in this article will be that of writing a function on the right of its argument, e.g.
