 | Look up indeterminate in Wiktionary, the free dictionary. |
Indeterminate may refer to:
| Look up indeterminate in Wiktionary, the free dictionary. |
Indeterminate may refer to:
In mathematics, and particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else but itself and is used as a placeholder in objects such as polynomials and formal power series. In particular, it does not designate a constant or a parameter of the problem, it is not an unknown that could be solved for, and it is not a variable designating a function argument or being summed or integrated over; it is not any type of bound variable.
An indeterminate system is a system of simultaneous equations which has more than one solution. The system may be said to be underspecified. If the system is linear, then the presence of more than one solution implies that there are an infinite number of solutions, but that property does not extend to nonlinear systems.
An indeterminate equation, in mathematics, is an equation for which there is more than one solution; for example, 2x = y is a simple indeterminate equation, as are ax + by = c and x2 = 1. Indeterminate equations cannot be solved uniquely. Prominent examples include the following:
In biology and botany, indeterminate growth is growth that is not terminated in contrast to determinate growth that stops once a genetically pre-determined structure has completely formed. Thus, a plant that grows and produces flowers and fruit until killed by frost or some other external factor is called indeterminate. For example, the term is applied to tomato varieties that grow in a rather gangly fashion, producing fruit throughout the growing season, and in contrast to a determinate tomato plant, which grows in a more bushy shape and is most productive for a single, larger harvest, then either tapers off with minimal new growth or fruit, or dies.
Indeterminacy, in philosophy, can refer both to common scientific and mathematical concepts of uncertainty and their implications and to another kind of indeterminacy deriving from the nature of definition or meaning. It is related to deconstructionism and to Nietzsche's criticism of the Kantian noumenon.
Indeterminacy is a composing approach in which some aspects of a musical work are left open to chance or to the interpreter's free choice. John Cage, a pioneer of indeterminacy, defined it as "the ability of a piece to be performed in substantially different ways".
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In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied. A linear Diophantine equation equates the sum of two or more monomials, each of degree 1 in one of the variables, to a constant. An exponential Diophantine equation is one in which exponents on terms can be unknowns.
In mathematics, an equation is a statement that asserts the equality of two expressions. The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English any equality is an equation.
Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics. It is typically taught to secondary school students and builds on their understanding of arithmetic. Whereas arithmetic deals with specified numbers, algebra introduces quantities without fixed values, known as variables. This use of variables entails a use of algebraic notation and an understanding of the general rules of the operators introduced in arithmetic. Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers.
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7. An example in three variables is x3 + 2xyz2 − yz + 1.
In mathematics, a system of linear equations is a collection of two or more linear equations involving the same set of variables. For example,
Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. Prior to quantum physics, it was thought that
In mathematics, to solve an equation is to find its solutions, which are the values that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign. When seeking a solution, one or more free variables are designated as unknowns. A solution is an assignment of expressions to the unknown variables that makes the equality in the equation true. In other words, a solution is an expression or a collection of expressions such that, when substituted for the unknowns, the equation becomes an identity. A solution of an equation is often also called a root of the equation, particularly but not only for algebraic or numerical equations.
In statics, a structure is statically indeterminate when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure.
In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems. Its modern version formulated in terms of the members' flexibility matrices also has the name the matrix force method due to its use of member forces as the primary unknowns.
In elementary mathematics, a variable is a symbol, commonly a single letter, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown. Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation. A typical example is the quadratic formula, which allows one to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation for the variables that represent them.
An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. The concept typically arises in the context of linear equations. If it is possible to duplicate one of the equations in a system by multiplying each of the other equations by some number and summing the resulting equations, then that equation is dependent on the others. But if this is not possible, then that equation is independent of the others.
In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns. An overdetermined system is almost always inconsistent when constructed with random coefficients. However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others.
In mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns. The terminology can be explained using the concept of constraint counting. Each unknown can be seen as an available degree of freedom. Each equation introduced into the system can be viewed as a constraint that restricts one degree of freedom.
Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval. Time translation symmetry is the hypothesis that the laws of physics are unchanged, under such a transformation. Time translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time translation symmetry is closely connected, via the Noether theorem, to conservation of energy. In mathematics, the set of all time translations on a given system form a Lie group.