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A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...

Pre-Algebra

In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

Two lengths are called incommensurate or incommensurable if their ratio cannot be expressed as a ratio of whole numbers. Irrational numbers and transcendental numbers are ...

Pythagoras's theorem states that the diagonal d of a square with sides of integral length s cannot be rational. Assume d/s is rational and equal to p/q where p and q are ...

The quantum of a finite floating-point representation is the value of a unit in the last position of its significand. In general, the quantum is equal to the radix raised to ...

In floating-point arithmetic, the significand is a component of a finite floating-point number containing its significant digits. Generally speaking, the significand can be ...

In the IEEE 754-2008 standard (referred to as IEEE 754 henceforth), a floating-point representation is an unencoded member of a floating-point format which represents either ...