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... Our motivation for this problem arose from counting certain finite topologies as described below. If j is any point in a finite topological space, let N (j) be the intersection of all open sets containing j. Corollary. Let T be the set of topologies τ on n such that the basis {N (j) : j ∈ n} consist ...
... Our motivation for this problem arose from counting certain finite topologies as described below. If j is any point in a finite topological space, let N (j) be the intersection of all open sets containing j. Corollary. Let T be the set of topologies τ on n such that the basis {N (j) : j ∈ n} consist ...
JSUNIL TUTORIAL, SAMASTIPUR ...
... 1. For what value of „a‟ the number -11/a is not a rational number. ( a) -1 (b) 1 (c) 0 (d) 10 ...
... 1. For what value of „a‟ the number -11/a is not a rational number. ( a) -1 (b) 1 (c) 0 (d) 10 ...
IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN:2319-765X.
... Squares of integers can be expressed as sum of consecutive odd numbers. Is there a general case for all powers? After a thorough search with available materials I could not find one such theorem. Here is an attempt in that lines. Sum of consecutive odd numbers as powers of integers and sum of consec ...
... Squares of integers can be expressed as sum of consecutive odd numbers. Is there a general case for all powers? After a thorough search with available materials I could not find one such theorem. Here is an attempt in that lines. Sum of consecutive odd numbers as powers of integers and sum of consec ...
Number Systems, Operations, and Codes
... Hexadecimal Numbers If you see ‘h’ mixing in numbers (in the context of computer systems), please note that it’s most likely that the numbers are hexadecimal numbers. (Be careful. ‘h’ is not one of A-F using in hex). ...
... Hexadecimal Numbers If you see ‘h’ mixing in numbers (in the context of computer systems), please note that it’s most likely that the numbers are hexadecimal numbers. (Be careful. ‘h’ is not one of A-F using in hex). ...
6. The transfinite ordinals* 6.1. Beginnings
... 6.3. Ordinal arithmetic We’ve been deriving our notation for ordinal numbers by using arithmetical operations; evidently it would be as well to have some idea of how these work. The principles of ordinal arithmetic are fundamentally different from those of cardinal arithmetic, in that they are all a ...
... 6.3. Ordinal arithmetic We’ve been deriving our notation for ordinal numbers by using arithmetical operations; evidently it would be as well to have some idea of how these work. The principles of ordinal arithmetic are fundamentally different from those of cardinal arithmetic, in that they are all a ...
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.