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  2. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    The factorial of is , or in symbols, ! =. There are several motivations for this definition: For n = 0 {\displaystyle n=0} , the definition of n ! {\displaystyle n!} as a product involves the product of no numbers at all, and so is an example of the broader convention that the empty product , a product of no factors, is equal to the ...

  3. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.

  4. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    (the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols). ⊃ {\displaystyle \supset } may mean the same as ⇒ {\displaystyle \Rightarrow } (the symbol may also mean superset ).

  5. 0 - Wikipedia

    en.wikipedia.org/wiki/0

    Zero was not treated as a number at that time, but as a "vacant position". [39] Qín Jiǔsháo's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol ‘〇’ for zero. [40] The origin of this symbol is unknown; it may have been produced by modifying a square symbol. [41]

  6. Empty product - Wikipedia

    en.wikipedia.org/wiki/Empty_product

    For example, the empty products 0! = 1 (the factorial of zero) and x 0 = 1 shorten Taylor series notation (see zero to the power of zero for a discussion of when x = 0). Likewise, if M is an n × n matrix, then M 0 is the n × n identity matrix , reflecting the fact that applying a linear map zero times has the same effect as applying the ...

  7. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    (α) to most complex numbers z, this definition has the feature of working for all positive real values of α. Furthermore, when α = 1, this definition is mathematically equivalent to the Π(z) function, described above. Also, when α = 2, this definition is mathematically equivalent to the alternative extension of the double factorial.

  8. Falling and rising factorials - Wikipedia

    en.wikipedia.org/wiki/Falling_and_rising_factorials

    In this article, the symbol () is used to represent the falling factorial, and the symbol () is used for the rising factorial. These conventions are used in combinatorics , [ 4 ] although Knuth 's underline and overline notations x n _ {\displaystyle x^{\underline {n}}} and x n ¯ {\displaystyle x^{\overline {n}}} are increasingly popular.

  9. Mathematical operators and symbols in Unicode - Wikipedia

    en.wikipedia.org/wiki/Mathematical_operators_and...

    greek beta symbol u+03d1: ϑ: greek theta symbol u+03d2: ϒ: greek upsilon with hook symbol u+03d5: ϕ: greek phi symbol u+03f0: ϰ: greek kappa symbol u+03f1: ϱ: greek rho symbol u+03f4: ϴ: greek capital theta symbol u+03f5: ϵ: greek lunate epsilon symbol u+03f6 ϶ greek reversed lunate epsilon symbol