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The number e (e = 2.71828...), also known as Euler's number, which occurs widely in mathematical analysis The number i , the imaginary unit such that i 2 = − 1 {\displaystyle i^{2}=-1} The equation is often given in the form of an expression set equal to zero, which is common practice in several areas of mathematics.
A similar problem, involving equating like terms rather than coefficients of like terms, arises if we wish to de-nest the nested radicals + to obtain an equivalent expression not involving a square root of an expression itself involving a square root, we can postulate the existence of rational parameters d, e such that
Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables and .The area contained by both circles is the joint entropy (,).
The relationship x precedes y is written x ≺ y. The relation x precedes or is equal to y is written x ≼ y. The relationship x succeeds (or follows) y is written x ≻ y. The relation x succeeds or is equal to y is written x ≽ y. [citation needed]
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
ln(r) is the standard natural logarithm of the real number r. Arg(z) is the principal value of the arg function; its value is restricted to (−π, π]. It can be computed using Arg(x + iy) = atan2(y, x). Log(z) is the principal value of the complex logarithm function and has imaginary part in the range (−π, π].
The equivalence relations on any set X, when ordered by set inclusion, form a complete lattice, called Con X by convention. The canonical map ker : X^X → Con X, relates the monoid X^X of all functions on X and Con X. ker is surjective but not injective. Less formally, the equivalence relation ker on X, takes each function f : X → X to its ...
A binary equaliser (that is, an equaliser of just two functions) is also called a difference kernel.This may also be denoted DiffKer(f, g), Ker(f, g), or Ker(f − g).The last notation shows where this terminology comes from, and why it is most common in the context of abstract algebra: The difference kernel of f and g is simply the kernel of the difference f − g.