Concept

Exponentiation

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Recursive definition

In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs.

Principal branch

In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function. Most often, this applies to functions defined on the complex plane. Principal branches are used in the definition of many inverse trigonometric functions, such as the selection either to define that or that A more familiar principal branch function, limited to real numbers, is that of a positive real number raised to the power of 1/2. For example, take the relation y = x1/2, where x is any positive real number.

Prime power

In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number. For example: 7 = 7^1, 9 = 3^2 and 64 = 2^6 are prime powers, while 6 = 2 × 3, 12 = 2^2 × 3 and 36 = 6^2 = 2^2 × 3^2 are not. The sequence of prime powers begins: 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, .

Robert Recorde

Robert Recorde (1512 – 1558) was a Welsh physician and mathematician. He invented the equals sign (=) and also introduced the pre-existing plus (+) and minus (−) signs to English speakers in 1557. Born around 1512, Robert Recorde was the second and last son of Thomas and Rose Recorde of Tenby, Pembrokeshire, in Wales. Recorde entered the University of Oxford about 1525, and was elected a Fellow of All Souls College there in 1531. Having adopted medicine as a profession, he went to the University of Cambridge to take the degree of M.

Fourth power

In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: n4 = n × n × n × n Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n4 as n “Tesseracted”, “Hypercubed”, “Zenzizenzic”, “Biquadrate” or “Supercubed” instead of “to the power of 4”.

Caret

Caret is the name used familiarly for the character , (the circumflex and a circumflex accent) provided on most QWERTY keyboards by typing . The symbol has a variety of uses in programming and mathematics. The name "caret" arose from its visual similarity to the original proofreader's caret, a mark used in proofreading to indicate where a punctuation mark, word, or phrase should be inserted into a document. The formal ASCII standard (X3.64.1977) calls it a "circumflex".

Like terms

In mathematics, like terms are summands in a sum that differ only by a numerical factor. Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression, like terms are those that contain the same variables to the same powers, possibly with different coefficients. More generally, when some variable are considered as parameters, like terms are defined similarly, but "numerical factors" must be replaced by "factors depending only on the parameters".

P-adic valuation

In number theory, the p-adic valuation or p-adic order of an integer n is the exponent of the highest power of the prime number p that divides n. It is denoted . Equivalently, is the exponent to which appears in the prime factorization of . The p-adic valuation is a valuation and gives rise to an analogue of the usual absolute value. Whereas the completion of the rational numbers with respect to the usual absolute value results in the real numbers , the completion of the rational numbers with respect to the -adic absolute value results in the p-adic numbers .