The Fibonacci Numbers And An Unexpected Calculation.
... A program P prints out the infinite sequence s0, s1, s2, …, sk, … if when P is executed on an ideal computer, it outputs a sequence of symbols such that -The kth symbol that it outputs is sk -For every k2, P eventually outputs the kth symbol. I.e., the delay between symbol k and symbol k+1 is not i ...
... A program P prints out the infinite sequence s0, s1, s2, …, sk, … if when P is executed on an ideal computer, it outputs a sequence of symbols such that -The kth symbol that it outputs is sk -For every k2, P eventually outputs the kth symbol. I.e., the delay between symbol k and symbol k+1 is not i ...
Functions
... Sets A and B have the same cardinality iff there is a oneto-one correspondence from A to B. We denote A and B have the same cardinality by |A| = |B|. ...
... Sets A and B have the same cardinality iff there is a oneto-one correspondence from A to B. We denote A and B have the same cardinality by |A| = |B|. ...
Ithaca College Math Day Competition April 18, 2007 Part I
... 7. Call a number “prime-looking” if it is composite but not divisible by 2, 3, or 5. The three smallest prime-looking numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many prime-looking numbers are there less than 1000? (Recall that a composite number is any integer greate ...
... 7. Call a number “prime-looking” if it is composite but not divisible by 2, 3, or 5. The three smallest prime-looking numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many prime-looking numbers are there less than 1000? (Recall that a composite number is any integer greate ...
Chapter 11: The Non-Denumerability of the Continuum
... The interval of all real numbers between 0 and 1 is denumerable. Proof: By contradiction, we have proved this to be false. Therefore the interval of real numbers between 0 and 1 is NOT denumerable. Some skeptics may argue that, although b may not have existed in the left-hand column, it would be eas ...
... The interval of all real numbers between 0 and 1 is denumerable. Proof: By contradiction, we have proved this to be false. Therefore the interval of real numbers between 0 and 1 is NOT denumerable. Some skeptics may argue that, although b may not have existed in the left-hand column, it would be eas ...
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.