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In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. [1] Both are special cases of a more general function of a matrix called the immanant.
A mathematical object is an abstract concept arising in mathematics. [1] Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas.
The irresistible force paradox (also unstoppable force paradox or shield and spear paradox), is a classic paradox formulated as "What happens when an unstoppable force meets an immovable object?"
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...
In computer science, having value semantics (also value-type semantics or copy-by-value semantics) means for an object that only its value counts, not its identity. [1] [2] Immutable objects have value semantics trivially, [3] and in the presence of mutation, an object with value semantics can only be uniquely-referenced at any point in a program.
Making a shallow copy of a const or immutable value removes the outer layer of immutability: Copying an immutable string (immutable(char[])) returns a string (immutable(char)[]). The immutable pointer and length are being copied and the copies are mutable. The referred data has not been copied and keeps its qualifier, in the example immutable.
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
The preceding kinds of definitions, which had prevailed since Aristotle's time, [4] were abandoned in the 19th century as new branches of mathematics were developed, which bore no obvious relation to measurement or the physical world, such as group theory, projective geometry, [3] and non-Euclidean geometry.