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In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
Exponentiation for a natural power is defined as iterated multiplication, which Knuth denoted by a single up-arrow: a ↑ b = H 3 ( a , b ) = a b = a × a × ⋯ × a ⏟ b copies of a {\displaystyle {\begin{matrix}a\uparrow b=H_{3}(a,b)=a^{b}=&\underbrace {a\times a\times \dots \times a} \\&b{\mbox{ copies of }}a\end{matrix}}}
Mathematical Alphanumeric Symbols is a Unicode block comprising styled forms of Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The letters in various fonts often have specific, fixed meanings in particular areas of mathematics.
In 2017, it was proven [14] that there exists a unique function F which is a solution of the equation F(z + 1) = exp(F(z)) and satisfies the additional conditions that F(0) = 1 and F(z) approaches the fixed points of the logarithm (roughly 0.318 ± 1.337i) as z approaches ±i∞ and that F is holomorphic in the whole complex z-plane, except the ...
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
A mathematical coincidence often involves an integer, and the surprising feature is the fact that a real number arising in some context is considered by some standard as a "close" approximation to a small integer or to a multiple or power of ten, or more generally, to a rational number with a small denominator.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
The sum of the reciprocals of the squared powers of two (powers of four) is 1/3. The smallest natural power of two whose decimal representation begins with 7 is [11] = Every power of 2 (excluding 1) can be written as the sum of four square numbers in 24 ways. The powers of 2 are the natural numbers greater than 1 that can be written as the sum ...