Internal Inconsistency and the Reform of Naïve Set Comprehension
... numbers. The next highest ordinal is itself an ordinal (because of its own description) and (by definition based on the concept of the ordering of the series of ordinals) larger not only than all ordinals including its immediate predecessor (the set of all ordinals) but also than itself. In this cas ...
... numbers. The next highest ordinal is itself an ordinal (because of its own description) and (by definition based on the concept of the ordering of the series of ordinals) larger not only than all ordinals including its immediate predecessor (the set of all ordinals) but also than itself. In this cas ...
Coinductive Definitions and Real Numbers
... keeps track of possible rounding errors that might have been introduced during the computation. It produces two floating point numbers: the first is the result obtained using normal floating point arithmetic while the second gives the range about this point that the exact result is guaranteed to be ...
... keeps track of possible rounding errors that might have been introduced during the computation. It produces two floating point numbers: the first is the result obtained using normal floating point arithmetic while the second gives the range about this point that the exact result is guaranteed to be ...
significant digits worksheet
... Any zero printed to the right of a non-zero digit may or may not be significant if there is no decimal point indicated. For example, if someone tells you that a mountain is 3600 m high they are probably certain of the 3, and uncertain of the 6. In other words, there are likely 2 significant digits. ...
... Any zero printed to the right of a non-zero digit may or may not be significant if there is no decimal point indicated. For example, if someone tells you that a mountain is 3600 m high they are probably certain of the 3, and uncertain of the 6. In other words, there are likely 2 significant digits. ...
On integers of the forms k ± 2n and k2 n ± 1
... odd integers. On the other hand, Sierpiński [34] proved that there are infinitely many positive odd numbers k for which all k2n + 1 (n = 1, 2, . . .) are composite. In 1962, J.L. Selfridge (unpublished) discovered that for any positive integer n, the integer 78 557 · 2n + 1 is divisible by one of t ...
... odd integers. On the other hand, Sierpiński [34] proved that there are infinitely many positive odd numbers k for which all k2n + 1 (n = 1, 2, . . .) are composite. In 1962, J.L. Selfridge (unpublished) discovered that for any positive integer n, the integer 78 557 · 2n + 1 is divisible by one of t ...
Exploring Fibonacci Numbers
... Fibonacci learned how to perform calculations with these foreign numbers, he integrated them into his business practices. Throughout many years of traveling as a merchant, Fibonacci grew to believe that the Hindu-Arabic numbers demonstrated superiority over Roman numerals in many ways. Motivated by ...
... Fibonacci learned how to perform calculations with these foreign numbers, he integrated them into his business practices. Throughout many years of traveling as a merchant, Fibonacci grew to believe that the Hindu-Arabic numbers demonstrated superiority over Roman numerals in many ways. Motivated by ...
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.