Search results
Results From The WOW.Com Content Network
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
In mathematics, an index set is a set whose members label (or index) members of another set. [ 1 ] [ 2 ] For instance, if the elements of a set A may be indexed or labeled by means of the elements of a set J , then J is an index set.
For example: "All humans are mortal, and Socrates is a human. ∴ Socrates is mortal." ∵ Abbreviation of "because" or "since". Placed between two assertions, it means that the first one is implied by the second one. For example: "11 is prime ∵ it has no positive integer factors other than itself and one." ∋ 1. Abbreviation of "such that".
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:
In mathematics, a family, or indexed family, is informally a collection of objects, each associated with an index from some index set.For example, a family of real numbers, indexed by the set of integers, is a collection of real numbers, where a given function selects one real number for each integer (possibly the same) as indexing.
A subgroup H of finite index in a group G (finite or infinite) always contains a normal subgroup N (of G), also of finite index. In fact, if H has index n, then the index of N will be some divisor of n! and a multiple of n; indeed, N can be taken to be the kernel of the natural homomorphism from G to the permutation group of the left (or right ...
For example, the S&P 500 index represents the 500 largest publicly traded U.S. companies. The Russell 2000, on the other hand, tracks the 2,000 smallest companies on the Russell 3000 index.
In mathematics, an n th root of a number x is a number r which, when raised to the power of n, yields x: = ⏟ =. The positive integer n is called the index or degree, and the number x of which the root is taken is the radicand.