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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]
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 types, many symbols are needed for ...
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.
Because a solution to a linear system must satisfy all of the equations, the solution set is the intersection of these lines, and is hence either a line, a single point, or the empty set. For three variables, each linear equation determines a plane in three-dimensional space , and the solution set is the intersection of these planes.
wff – well-formed formula. whp – with high probability. wlog – without loss of generality. WMA – we may assume. WO – well-ordered set. [1] WOP – well-ordered principle. w.p. – with probability. wp1 – with probability 1. wrt – with respect to or with regard to. WTP – want to prove. WTS – want to show.
The formula calculator concept can be applied to all types of calculator, including arithmetic, scientific, statistics, financial and conversion calculators. The calculation can be typed or pasted into an edit box of: A software package that runs on a computer, for example as a dialog box. An on-line formula calculator hosted on a web site.
It should be also noted that even characterising the solution set of a single word equation is complicated. Hmelevskii [9] proved that, although the solutions to three-unknown constant-free equations can be given in terms of finite expressions with word and integer parameters, this is not true (in general) for four-unknown constant-free equations.
A binary equaliser (that is, an equaliser of just two functions) is also called a difference kernel.This may also be denoted DiffKer(f, g), Ker(f, g), or Ker(f − g).The last notation shows where this terminology comes from, and why it is most common in the context of abstract algebra: The difference kernel of f and g is simply the kernel of the difference f − g.