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.
Another 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 MoreWilliam Jones, a mathematics teacher, first came up with pi; however, Leonard Euler is often credited with its introduction into mathematics. Jones wrote in his second book "Synopsis" that he believed pi was actually an irrational number, and the ratio should be represented by a symbol.
Full Answer >In mathematics, a variable is a symbol used for a number not yet known, while a constant is a number or symbol that has a fixed value. The value of a variable can change depending on the equation, while the value of a constant always remains the same.
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, 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.
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