Search results
Results from the WOW.Com Content Network
The left end consisted of electromechanical computing components. The right end included data and program readers, and automatic typewriters. The Harvard Mark I, or IBM Automatic Sequence Controlled Calculator (ASCC), was one of the earliest general-purpose electromechanical computers used in the war effort during the last part of World War II.
The complete sequences include: The sequence of the number 1 followed by the prime numbers (studied by S. S. Pillai [3] and others); this follows from Bertrand's postulate. [1] The sequence of practical numbers which has 1 as the first term and contains all other powers of 2 as a subset. [4] (sequence A005153 in the OEIS)
Here the nth term in the sequence is the nth decimal approximation for pi. Though this is a Cauchy sequence of rational numbers, it does not converge to any rational number. (In this real number line, this sequence converges to pi.) Cauchy completeness is related to the construction of the real numbers using Cauchy sequences.
The parity sequence is the same as the sequence of operations. Using this form for f(n), it can be shown that the parity sequences for two numbers m and n will agree in the first k terms if and only if m and n are equivalent modulo 2 k. This implies that every number is uniquely identified by its parity sequence, and moreover that if there are ...
When the user is unsure how a calculator will interpret an expression, parentheses can be used to remove the ambiguity. [ 3 ] Order of operations arose due to the adaptation of infix notation in standard mathematical notation , which can be notationally ambiguous without such conventions, as opposed to postfix notation or prefix notation ...
These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic. Since the publishing of Gödel's paper in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects.
The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. [1] This produces a sequence where the ratios of successive terms approach the golden ratio, and in fact the terms themselves are roundings of integer powers of the golden ...
For generalized Fibonacci sequences (satisfying the same recurrence relation, but with other initial values, e.g. the Lucas numbers) the number of occurrences of 0 per cycle is 0, 1, 2, or 4. The ratio of the Pisano period of n and the number of zeros modulo n in the cycle gives the rank of apparition or Fibonacci entry point of n .