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Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in the Wolfram ...

If and only if (i.e., necessary and sufficient). The terms "just if" or "exactly when" are sometimes used instead. A iff B is written symbolically as A<->B, A<=>B, A<->B, or ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

A disjunction that is true if only one, but not both, of its arguments are true, and is false if neither or both are true, which is equivalent to the XOR connective. By ...

A disjunction that remains true if either or both of its arguments are true. This is equivalent to the OR connective. By contrast, the exclusive disjunction is true if only ...

If a matrix group is reducible, then it is completely reducible, i.e., if the matrix group is equivalent to the matrix group in which every matrix has the reduced form ...

Two patterns T_1 and T_2 belong to the same Wilf class if |S_n(T_1)|=|S_n(T_2)| for all n, where S_n(T) denotes the set of permutations on {1,...,n} that avoid the pattern T. ...

Let phi(x_1,...,x_m) be an L_(exp) formula, where L_(exp)=L union {e^x} and L is the language of ordered rings L={+,-,·,<,0,1}. Then there exist n>=m and f_1,...,f_s in ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

The symbol used to separate the integer part of a decimal number from its fractional part is called the decimal point. In the United States, the decimal point is denoted with ...