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... Since these results hold for all integers k J> ls we see that there are an infinite number of heptagonal numbers which are, at the same time9 the sums and differences of distinct heptagonal numbers. Q.E.D. For k = 1, 2, and 3 9 respectively9 Theorem 2 yields ...
... Since these results hold for all integers k J> ls we see that there are an infinite number of heptagonal numbers which are, at the same time9 the sums and differences of distinct heptagonal numbers. Q.E.D. For k = 1, 2, and 3 9 respectively9 Theorem 2 yields ...
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.