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A binary operation f(x,y) is an operation that applies to two quantities or expressions x and y. A binary operation on a nonempty set A is a map f:A×A->A such that 1. f is ...

Exponentiation is the process of taking a quantity b (the base) to the power of another quantity e (the exponent). This operation most commonly denoted b^e. In TeX, the ...

The commutation operation [a,b]=ab-ba corresponding to the Lie product.

The multiplication operation corresponding to the Lie bracket.

The number of nonassociative n-products with k elements preceding the rightmost left parameter is F(n,k) = F(n-1,k)+F(n-1,k-1) (1) = (n+k-2; k)-(n+k-1; k-1), (2) where (n; k) ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

The natural projection, also called the homomorphism, is a logical way of mapping an algebraic structure onto its quotient structures. The natural projection pi is defined ...

Consider the expression 3×7+2^2. This expression has value (3×7)+(2^2)=25 due to what is called operator precedence (or "order of operations"). Precedence of common operators ...

Two fractions are said to be adjacent if their difference has a unit numerator. For example, 1/3 and 1/4 are adjacent since 1/3-1/4=1/12, but 1/2 and 1/5 are not since ...

Cahen's constant is defined as C = sum_(k=0)^(infty)((-1)^k)/(a_k-1) (1) = 0.64341054628... (2) (OEIS A118227), where a_k is the kth term of Sylvester's sequence.