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Much of what follows might be review, but it is very important that you are fluent in the language of set theory. Most of the notation we use below is standard, although some might be a little different than what you have seen before. For us, a set will simply be an unordered collection of objects.
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Two examples: we could consider the set of all actors who have played The Doctor on Doctor Who , or the set of natural numbers between 1 and 10 inclusive. In the first case, Tom Baker is a element or member of the set, while Idris Elba, among many others, is not an element of the set. Also, the two examples are of different sets.
Two sets are equal exactly if they contain the exact same elements. Some more notation:.
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This is a strange set, to be sure. We have described the sets above by listing their elements. Sometimes this is hard to do, especially when there are a lot of elements in the set perhaps infinitely many. Slightly easier might be,. Defining a set using this sort of notation is very useful, although it takes some practice to read them correctly. Here are some more examples:. Describe each of the following sets both in words and by listing out enough elements to see the pattern.
This is the set of all numbers which are 3 less than a natural number i. This is the set of all natural numbers which are 3 less than a natural number. There is only one: 0. We already have a lot of notation, and there is more yet.
Below is a handy chart of symbols. Views Total views. Actions Shares. Embeds 0 No embeds. No notes for slide. Introduction to Sets 1.
The second way of writing set is to use a property that defines elements of the set. N- set of all natural numbers b. Z- set of all integers c.source
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Q- set of all rational numbers d. R- set of all real numbers e. C- set of all complex numbers 5. Therefore, it is an empty set.
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Here B is an empty set because there is no composite number less than 4. Empty set is also called a finite set. It is denoted by n A. Clearly, A and B do not have any element in common and are disjoint sets. It is denoted by P A. In P A , every element is a set.