In mathematics, a well-defined set clearly indicates what is a member of the set and what is not. For example, a set that is identified as "the set of even whole numbers between 1 and 11" is a well-defined set because it is possible to identify the exact members of the set: 2, 4, 6, 8 and 10. There is only one possible solution set that fits this description.
Continue ReadingAnother example of a well-defined set is "the set of integers from -3 to 3, inclusive." This set clearly contains -3, -2, -1, 0, 1, 2 and 3 and only those integers.
On the other hand, "the set of lucky numbers" is not well-defined because it is open to interpretation. It is not clear from the description what "lucky" means, whose lucky numbers will be considered and what has to happen for a number to be considered "lucky." There are any number of possible solution sets.
In set theory, it does not matter how the members of the set are arranged. Therefore, {2, 3, 4, 6, 8, 10} is identical to {10, 2, 4, 8, 6, 3}. It does not affect the well-defined nature of a set.
When discussing sets, the "order" of the sets does not refer to their arrangement but to their sizes. "The set of even whole numbers between 1 and 11" has an order of 6.
Learn more about AlgebraA term in mathematics is defined as a number, variable or number-variable combination in an algebraic expression or equation. Terms are separated from each other by a plus, minus or equal sign.
Full Answer >Elimination in mathematics refers to the elimination method, also called the addition method, which is used to solve basic algebraic problems by comparing two equations in order to find what their variables equal. This method uses two equations to cancel out a variable in one of the equations.
Full Answer >A scale in mathematics refers to the ratio of a drawing in comparison to the size of the real object. A ratio is a relative size that represents typically two values. For example, 1:3 pears and grapefruits represents that there is one pear for every three grapefruit.
Full Answer >In certain applications of mathematics, particularly in business math and economics, the law of variable proportions states that the marginal product of a factor, when increased by itself, will eventually start to decline. In other words, increasing a single factor of production, such as labor or equipment, without increasing other related factors will lead to an increase in marginal product followed by an inevitable decrease.
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