Why is the concepts of sets important in mathematics

Transitive Relation on Set : What is transitive relation on set? Equivalence Relation on Set : What is equivalence relation on set? Learn step-by step to get the equivalence relation in the basic concepts of sets using solved examples. Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need. Worksheet on Set. Worksheet on Set Theory.

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Inclusion is an order relation. Functions of various kinds are ubiquitous in mathematics and a large vocabulary has developed, some of which is redundant. The term map is often used as an alternative for function and when the domain and codomain coincide the term transformation is often used instead of function. There is large number of terms for functions in particular context with special properties.

We start with the simplest examples of sets. The empty set a. Clearly, there is exactly one empty set. Next up are the singletons. It takes an introduction to logic to understand this, but this statement is one that is "vacuously" or "trivially" true. A good way to think about it is: we can't find any elements in the empty set that aren't in A , so it must be that all elements in the empty set are in A.

No, not the order of the elements. In sets it does not matter what order the elements are in. A finite set has finite order or cardinality. An infinite set has infinite order or cardinality. For infinite sets, all we can say is that the order is infinite. Oddly enough, we can say with sets that some infinities are larger than others, but this is a more advanced topic in sets. Hide Ads About Ads. Introduction to Sets Forget everything you know about numbers.

In fact, forget you even know what a number is. This is where mathematics starts. Instead of math with numbers, we will now think about math with "things". When talking about sets, it is fairly standard to use Capital Letters to represent the set, and lowercase letters to represent an element in that set.

So for example, A is a set, and a is an element in A. Same with B and b, and C and c. Example: Are these sets equal? They both contain exactly the members 1, 2 and 3. It doesn't matter where each member appears, so long as it is there. A is a subset of B if and only if every element of A is in B.

So far so good. The following result is straightforward and very convenient for proving equality between sets. This set clearly has no elements. Using Theorem 1.

Thus, we refer to the empty set.