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 in AlgebraIn mathematics, a function's domain is all the possible inputs that the function can accept without breaking and the range is all the possible outputs. A real life example of this is using a simple calculator to add two numbers together. The function is the sum of "n" plus "m," the domain is all real numbers and the output is also all real numbers.
Full Answer >William 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 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.
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 >