In mathematics, given two ordered sets A and B, one can induce a partial ordering on the Cartesian product A × B. Given two pairs (a1,b1) and (a2,b2) in A × B, one sets (a1,b1) ≤ (a2,b2) if and only if a1 ≤ a2 and b1 ≤ b2. This ordering is called the product order, or alternatively the coordinatewise order, or even the componentwise order.
Another possible ordering on A × B is the lexicographical order. Unlike the latter, the product order of two totally ordered sets is not total. For example, the pairs (0, 1) and (1, 0) are incomparable in the product order of 0 < 1 with itself. The lexicographic...
In computing, row-major order and column-major order describe methods for arranging multidimensional arrays in linear storage such as random access memory.
In row-major order, consecutive elements of the rows of the array are contiguous in memory; in column-major order, consecutive elements of the columns are contiguous.
Array layout is critical for correctly passing arrays between programs written in different languages. It is also important for performance when traversing an array because accessing array elements that are contiguous in memory is usually faster than accessing elements which are...
Hint
$$ \Huge{x>y}$$ then $$\huge{\frac{1}{y} > \frac{1}{x}}$$
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if α1, ..., αn are algebraic numbers which are linearly independent over the rational numbers ℚ, then eα1, ..., eαn are algebraically independent over ℚ; in other words the extension field ℚ(eα1, ..., eαn) has transcendence degree n over ℚ.
An equivalent formulation (Baker 1975, Chapter 1, Theorem 1.4), is the following: If α1, ..., αn are distinct algebraic numbers, then the exponentials eα1, ..., eαn are linearly independent over t...
