Floating-Point Arithmetic: Precision and Accuracy with Mathematica
... infinite set of real numbers within a computer of finite memory and of given word length; therefore, certain compromises have to be made. For example, Sqrt[2] represents some number which is approximately 1.41421. If we want to represent it exactly there is little choice but to leave it as Sqrt[2]. ...
... infinite set of real numbers within a computer of finite memory and of given word length; therefore, certain compromises have to be made. For example, Sqrt[2] represents some number which is approximately 1.41421. If we want to represent it exactly there is little choice but to leave it as Sqrt[2]. ...
The Real Numbers
... Thus the difference between z and 1 is arbitrarily small. It would create quite an unintuitive line if we decided to make z and 1 different real numbers. To fit in with our intuition, we must agree that z = 1. That means that some real numbers (precisely all those numbers with a finite decimal expan ...
... Thus the difference between z and 1 is arbitrarily small. It would create quite an unintuitive line if we decided to make z and 1 different real numbers. To fit in with our intuition, we must agree that z = 1. That means that some real numbers (precisely all those numbers with a finite decimal expan ...
Hypergeometric τ -functions, Hurwitz numbers and paths J. Harnad and A. Yu. Orlov
... In [12] a general method for interpreting 2D Toda τ -functions [32, 30, 31] of hypergeometric type [19, 29] as combinatorial generating functions for certain classes of paths in the Cayley graph of the symmetric group Sn was introduced. Examples included Okounkov’s generating function for double Hur ...
... In [12] a general method for interpreting 2D Toda τ -functions [32, 30, 31] of hypergeometric type [19, 29] as combinatorial generating functions for certain classes of paths in the Cayley graph of the symmetric group Sn was introduced. Examples included Okounkov’s generating function for double Hur ...
Full text
... The question then arises as to whether we can extend Stirling numbers to negative integral values of one or both of their arguments. Several authors have discussed the case where both n and k are negative integers (for a brief history, see Knuth [4]), and we briefly discuss this case in Section 3. W ...
... The question then arises as to whether we can extend Stirling numbers to negative integral values of one or both of their arguments. Several authors have discussed the case where both n and k are negative integers (for a brief history, see Knuth [4]), and we briefly discuss this case in Section 3. W ...
![arXiv:math/9205211v1 [math.HO] 1 May 1992](http://s1.studyres.com/store/data/017806193_1-68d48c35d33f53708478382611422518-300x300.png)
Algebra
... problems to real-world situations. Problems may relate to sports, meteorology, profit and loss, physics, health careers, electricity, or graphic design, just to name a few. To solve problems, you will need to write an equation, solve it, and check to make sure that the answer makes sense. The next s ...
... problems to real-world situations. Problems may relate to sports, meteorology, profit and loss, physics, health careers, electricity, or graphic design, just to name a few. To solve problems, you will need to write an equation, solve it, and check to make sure that the answer makes sense. The next s ...
Sets of Numbers
... 0.2 { 0, 1, 2, 3, … } is called the set of ___________________ 0.3 The set of rational numbers consists of ____________ and proper fractions or mixed numbers. Each of these numbers can be written as a fraction and have a terminating decimal expression or have a repeating part if it is nonterminating ...
... 0.2 { 0, 1, 2, 3, … } is called the set of ___________________ 0.3 The set of rational numbers consists of ____________ and proper fractions or mixed numbers. Each of these numbers can be written as a fraction and have a terminating decimal expression or have a repeating part if it is nonterminating ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.