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.
Know MoreAnother 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 AlgebraIn mathematics, linear refers to an equation or function that is the equation of a straight line and takes the form y = mx + b, where "m" is equal to the slope, and "b" is equal to the y-intercept. Three features define a function as linear, but if a function satisfies one of the three requirements, then it satisfies them all and can be classified as linear.
Full Answer >The fourth root of 16 is 2. In mathematics, the fourth root of a number is a number r that yields z when raised to power 4, where 4 is the degree of the root.
Full Answer >In mathematics, a function is a relation between a set of inputs and a set of permissible outputs. Specifically, each input into a function has exactly one corresponding and correct output.
Full Answer >In mathematics, a trivial solution is one that is considered to be very simple and poses little interest for the mathematician. Typical examples are solutions with the value 0 or the empty set, which does not contain any elements.
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