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The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and ...
In general, a Grassmann algebra on n generators can be represented by 2 n × 2 n square matrices. Physically, these matrices can be thought of as raising operators acting on a Hilbert space of n identical fermions in the occupation number basis. Since the occupation number for each fermion is 0 or 1, there are 2 n possible basis states ...
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
A quadratic equation is one which includes a term with an exponent of 2, for example, , [40] and no term with higher exponent. The name derives from the Latin quadrus , meaning square. [ 41 ] In general, a quadratic equation can be expressed in the form a x 2 + b x + c = 0 {\displaystyle ax^{2}+bx+c=0} , [ 42 ] where a is not zero (if it were ...
Since (y 2, z, x 2) form a primitive Pythagorean triple, they can be written z = 2de y 2 = d 2 − e 2 x 2 = d 2 + e 2. where d and e are coprime and d > e > 0. Thus, x 2 y 2 = d 4 − e 4. which produces another solution (d, e, xy) that is smaller (0 < d < x). As before, there must be a lower bound on the size of solutions, while this argument ...
Visualization of powers of two from 1 to 1024 (2 0 to 2 10) as base-2 Dienes blocks. A power of two is a number of the form 2 n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.
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