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Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables action=purge&mathpurge=true. Imagine for example there is a wrong rendered formula in the article Integral
A cheat sheet that is used contrary to the rules of an exam may need to be small enough to conceal in the palm of the hand Cheat sheet in front of a juice box. A cheat sheet (also cheatsheet) or crib sheet is a concise set of notes used for quick reference. Cheat sheets were historically used by students without an instructor or teacher's ...
Ackermann function: in the theory of computation, a computable function that is not primitive recursive. Dirac delta function: everywhere zero except for x = 0; total integral is 1. Not a function but a distribution, but sometimes informally referred to as a function, particularly by physicists and engineers.
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. [a] Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time ...
A partial function arises from the consideration of maps between two sets X and Y that may not be defined on the entire set X.A common example is the square root operation on the real numbers : because negative real numbers do not have real square roots, the operation can be viewed as a partial function from to .
They are summation functions (see the main section just below) of arithmetic functions which are neither multiplicative nor additive. π(x), the prime-counting function, is the number of primes not exceeding x. It is the summation function of the characteristic function of the prime numbers. =
The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).