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The sum-product conjecture informally says that one of the sum set or the product set of any set must be nearly as large as possible. It was originally conjectured by Erdős in 1974 to hold whether A is a set of integers, reals, or complex numbers. [3] More precisely, it proposes that, for any set A ⊂ ℂ, one has
In mathematics, specifically in group theory, the direct product is an operation that takes two groups G and H and constructs a new group, usually denoted G × H.This operation is the group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics.
The weighted product model (WPM) is a popular multi-criteria decision analysis (MCDA) / multi-criteria decision making (MCDM) method. It is similar to the weighted sum model (WSM) in that it produces a simple score, but has the very important advantage of overcoming the issue of 'adding apples and pears' i.e. adding together quantities measured in different units.
X and Y are two whole numbers greater than 1, and Y > X. Their sum is not greater than 100. S and P are two mathematicians (and consequently perfect logicians); S knows the sum X + Y and P knows the product X × Y. Both S and P know all the information in this paragraph. In the following conversation, both participants are always telling the truth:
The rule of sum is an intuitive principle stating that if there are a possible outcomes for an event (or ways to do something) and b possible outcomes for another event (or ways to do another thing), and the two events cannot both occur (or the two things can't both be done), then there are a + b total possible outcomes for the events (or total possible ways to do one of the things).
In this example a company should prefer product B's risk and payoffs under realistic risk preference coefficients. Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making (both in daily life and in settings such as business, government and medicine).
The natural numbers 0 and 1 are trivial sum-product numbers for all , and all other sum-product numbers are nontrivial sum-product numbers. For example, the number 144 in base 10 is a sum-product number, because 1 + 4 + 4 = 9 {\displaystyle 1+4+4=9} , 1 × 4 × 4 = 16 {\displaystyle 1\times 4\times 4=16} , and 9 × 16 = 144 {\displaystyle 9 ...
In decision theory, the weighted sum model (WSM), [1] [2] also called weighted linear combination (WLC) [3] or simple additive weighting (SAW), [4] is the best known and simplest multi-criteria decision analysis (MCDA) / multi-criteria decision making method for evaluating a number of alternatives in terms of a number of decision criteria.