What is a set?

The basic definition of a set refers to a collection of objects. A more precise and well-defined set describes any given object; we can objectively decide whether it is in the set, based on facts and not opinions.

Is it correct to say that a set is a collection of numbers or letters? Why yes or why not?

It is correct to say that a set is a collection of numbers or letters, but it is not limited to only those two elements. A set can describe days, months, colors, laws, etc.

What is an infinite set? Provide a minimum of two examples.

An infinite set is a set that is not finite; in other words, it has an unlimited number of elements. For example, the set {5,10,15,20,...} are equal since they is an infinite set since it contains an unlimited number of elements; the natural numbers that are multiples of 5. A second example of an infinite set is the set of all possible computer passwords; there are an unimaginable number of passwords.

What is the difference between equality and equivalence of sets? Support with a minimum of two examples.

An equal set contains two sets with precisely the same members, and an equivalent set contains two finite sets with the same number of elements. An example provided in the math textbook was that the two sets {a,b,c} and {c,b, a} are equal since they contain the same members a, b, and c. However, the set of all the names of students in a class and the set of the student ID numbers are equivalent because they have the same number of elements but different types of elements.

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