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Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
By using a dot to divide the digits into two groups, one can also write fractions in the positional system. For example, the base 2 numeral 10.11 denotes 1×2 1 + 0×2 0 + 1×2 −1 + 1×2 −2 = 2.75. In general, numbers in the base b system are of the form:
The set Γ of all open intervals in forms a basis for the Euclidean topology on .. A non-empty family of subsets of a set X that is closed under finite intersections of two or more sets, which is called a π-system on X, is necessarily a base for a topology on X if and only if it covers X.
The space K(ℓ 2) of compact operators on the Hilbert space ℓ 2 has a Schauder basis. For every x, y in ℓ 2, let x ⊗ y denote the rank one operator v ∈ ℓ 2 → <v, x > y. If {e n} n ≥ 1 is the standard orthonormal basis of ℓ 2, a basis for K(ℓ 2) is given by the sequence [17]
In the geometry of hyperbolic 3-space, the order-4-6 square honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {4,4,6}. It has six square tiling, {4,4}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many square tiling existing around each vertex in an ...
The Haar wavelet. In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis.
The monomial basis also forms a basis for the vector space of polynomials. After all, every polynomial can be written as a 0 + a 1 x 1 + a 2 x 2 + ⋯ + a n x n {\displaystyle a_{0}+a_{1}x^{1}+a_{2}x^{2}+\cdots +a_{n}x^{n}} for some n ∈ N {\displaystyle n\in \mathbb {N} } , which is a linear combination of monomials.
The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9.; The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).