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The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes . There are two canonical proofs that are always used to show non-mathematicians what a mathematical proof is like:
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
Re – real part of a complex number. [2] (Also written.) resp – respectively. RHS – right-hand side of an equation. rk – rank. (Also written as rank.) RMS, rms – root mean square. rng – non-unital ring. rot – rotor of a vector field. (Also written as curl.) rowsp – row space of a matrix. RTP – required to prove.
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.
The standard simplex or probability simplex [2] is the (k − 1)-dimensional simplex whose vertices are the k standard unit vectors in , or in other words {: + + =, =, …,}. In topology and combinatorics , it is common to "glue together" simplices to form a simplicial complex .
x is the argument of the complex number (angle between line to point and x-axis in polar form). The notation is less commonly used in mathematics than Euler's formula , e ix , which offers an even shorter notation for cos x + i sin x , but cis(x) is widely used as a name for this function in software libraries .
The complex numbers are a generalization of the real numbers, which are a generalization of the rational numbers, which are a generalization of the integers, which are a generalization of the natural numbers. A polygon is a generalization of a 3-sided triangle, a 4-sided quadrilateral, and so on to n sides.
A simplicial 3-complex. In mathematics, a simplicial complex is a structured set composed of points, line segments, triangles, and their n-dimensional counterparts, called simplices, such that all the faces and intersections of the elements are also included in the set (see illustration).