In mathematics, LHS is informal shorthand for the left-hand side of an equation. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent Similarly, RHS is the right-hand side. Each is solely a name for a term as part of an expression; and they are in practice interchangeable, since equality is symmetric. Equality is the paradigmatic example of the more general concept of Equivalence relations on a set those binary relations which are reflexive, symmetric In Mathematics, an equivalence relation is a Binary relation between two elements of a set which groups them together as being "equivalent" This abbreviation is seldom if ever used in print; it is very informal.
More generally, these terms may apply to an inequation or inequality. In Mathematics, an inequation is a statement that two objects or expressions are not the same or do not represent the same value In Mathematics, an inequality is a statement about the relative size or order of two objects or about whether they are the same or not (See also equality In the inequality case, there is no symmetry. The right-hand side is everything on the right side of a test operator in an expression. In Computer science a relational operator is a Programming language construct or operator that tests some kind of relation between two entities In mathematics the word expression is a term for any well-formed combination of mathematical symbols Conversely, the left-hand side is everything on the left side.
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Some examples
In
- 2a + 5 = a/3,
the term
- a/3
is the RHS. The word term is from the Latin terminus "boundary line limit" from the Indo-European root ter- "peg post boundary"
In
- x ≤ 10,
just
- 10
is the RHS.
Homogeneous and inhomogeneous equations
In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous is often used for equations with the RHS set equal to zero. In Mathematics, a system of linear equations (or linear system) is a collection of Linear equations involving the same set of Variables For example A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the In Mathematics, an integral equation is an equation in which an unknown function appears under an Integral sign The corresponding inhomogeneous or nonhomogeneous equation then has the RHS with some given data, but of a general character.
The typical case is of some operator L, with the difference being that between the equation
- Lf = 0,
to be solved for a function f, and the equation
- Lf = g,
with g a fixed function, to solve again for f. In Mathematics, an operator is a function which operates on (or modifies another function The point of the terminology appears for L a linear operator. In Mathematics, a linear map (also called a linear transformation, or linear operator) is a function between two Vector spaces that Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution.
For example in mathematical physics, the homogeneous equation may correspond to a physical theory formulated in empty space, while the inhomogeneous equation asks for more 'realistic' solutions with some matter, or charged particles. Mathematical physics is the scientific discipline concerned with the interface of Mathematics and Physics. Empty space may refer to Outer space, especially the relatively empty regions of the Universe outside the atmospheres of Celestial bodies
Syntax
More abstractly, when using infix notation
- T*U
the term T stands as the left-hand side and U as the right-hand side of the operator *. Infix notation is the common arithmetic and logical formula notation in which Operators are written Infix -style between the Operands they act on (e In Mathematics, an operator is a function which operates on (or modifies another function This usage is less common, though.
See also
History The "=" symbol that is now universally accepted by mathematics for equality was first recorded by Welsh mathematician Robert Recorde in TheDapyx Software network: MP3 Explorer | Ebook Manager | Zenithic