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We also have the rule that 10 x + y is divisible iff x + 4 y is divisible by 13. For example, to test the divisibility of 1761 by 13 we can reduce this to the divisibility of 461 by the first rule. Using the second rule, this reduces to the divisibility of 50, and doing that again yields 5. So, 1761 is not divisible by 13.
Two properties of 1001 are the basis of a divisibility test for 7, 11 and 13. The method is along the same lines as the divisibility rule for 11 using the property 10 ≡ -1 (mod 11). The two properties of 1001 are 1001 = 7 × 11 × 13 in prime factors 10 3 ≡ -1 (mod 1001) The method simultaneously tests for divisibility by any of the factors ...
The following laws can be verified using the properties of divisibility. They are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. As with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic ...
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. [1]
The height of a partially ordered set is defined to be the maximum cardinality of a chain, a totally ordered subset of the given partial order. For instance, in the set of positive integers from 1 to N, ordered by divisibility, one of the largest chains consists of the powers of two that lie within that range, from which it follows that the height of this partial order is + ⌊ ⌋.
o o o s. c: o thO 00 . Created Date: 9/20/2007 3:37:18 PM
The divisors of 10 illustrated with Cuisenaire rods: 1, 2, 5, and 10. In mathematics, a divisor of an integer , also called a factor of , is an integer that may be multiplied by some integer to produce . [1] In this case, one also says that is a multiple of .
In contract bridge, the Rule of 11 is applied when the opening lead is the fourth best from the defender's suit. [1] By subtracting the rank of the card led from 11, the partner of the opening leader can determine how many cards higher than the card led are held by declarer, dummy and himself; by deduction of those in dummy and in his own hand, he can determine the number in declarer's hand.