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A line is expressed as the intersection of two planes, that is as the solution set of a single linear equation with values in or as the solution set of two linear equations with values in . A conic section is the intersection of a cone with equation x 2 + y 2 = z 2 {\displaystyle x^{2}+y^{2}=z^{2}} and a plane.
In mathematics, the solution set of a system of equations or inequality is the set of all its solutions, that is the values that satisfy all equations and inequalities. [1] Also, the solution set or the truth set of a statement or a predicate is the set of all values that satisfy it. If there is no solution, the solution set is the empty set. [2]
In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas includes formulas in the language of second-order arithmetic , which can have quantifiers over both the set of natural numbers , N {\displaystyle \mathbb {N} } , and over functions from N ...
A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation is its solution set. An equation may be solved either numerically or symbolically. Solving an equation numerically means that only numbers are admitted as solutions.
Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
For example, the solution set for the above equation is a line, since a point in the solution set can be chosen by specifying the value of the parameter z. An infinite solution of higher order may describe a plane, or higher-dimensional set. Different choices for the free variables may lead to different descriptions of the same solution set.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
A stationary set is a subset of an ordinal intersecting every club set stratified A formula of set theory is stratified if and only if there is a function which sends each variable appearing in (considered as an item of syntax) to a natural number (this works equally well if all integers are used) in such a way that any atomic formula appearing ...