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Floyd's triangle is a triangular array of natural numbers used in computer science education. It is named after Robert Floyd . It is defined by filling the rows of the triangle with consecutive numbers, starting with a 1 in the top left corner:
The first ordinal number that is not a natural number is expressed as ω; this is also the ordinal number of the set of natural numbers itself. The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0 ) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω .
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
Transfinite numbers: Numbers that are greater than any natural number. Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets.
This is a list of all articles about natural numbers from 1 to 10,000. Red links are included to make it clearly visible which articles exist and which do not. Existing articles can either be articles with content, or redirects .
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In Zermelo–Fraenkel (ZF) set theory, the natural numbers are defined recursively by letting 0 = {} be the empty set and n + 1 (the successor function) = n ∪ {n} for each n. In this way n = {0, 1, …, n − 1} for each natural number n. This definition has the property that n is a set with n elements. The first few numbers defined this way ...
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