What is what? What Is Set? Related material Read more Cantor-Bernstein-Schroeder theorem. 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.
That's all the elements of A, and every single one is in B, so we're done. Example: Let A be all multiples of 4 and B be all multiples of 2. Is A a subset of B? And is B a subset of A? The empty set is a subset of every set, including the empty set itself. When we say order in sets we mean the size of the set. Another better name for this is cardinality. Or another example is types of fingers. This set includes index, middle, ring, and pinky. At the start we used the word "things" in quotes.
And in complex analysis, you guessed it, the universal set is the complex numbers. As the name implies, a set with a finite or countable number of elements is called a finite set. A set with an infinite number of elements is called an infinite set. A set that does not contain any element is called an empty set or a null set. It is read as ' phi '. If two sets have the same elements in them, then they are called equal sets. Here, set A and set B are equal sets. If two sets have at least one element that is different, then they are unequal sets.
Here, set A and set B are unequal sets. Two sets are said to be equivalent sets when they have the same number of elements, though the elements are different. Two sets are said to be overlapping if at least one element from set A is present in set B. Here, element 4 is present in set A as well as in set B. Therefore, A and B are overlapping sets.
Two sets are disjoint sets if there are no common elements in both sets. Here, set A and set B are disjoint sets. A universal set is the collection of all the elements in regard to a particular subject. The universal set is denoted by the letter 'U'. Here, a set of cars is a subset for this universal set, the set of cycles, trains are all subsets of this universal set.
Power set is the set of all subsets that a set could contain. Sets find their application in the field of algebra , statistics , and probability.
There are some important set formulas as listed below. For any two overlapping sets A and B,. Similar to numbers, sets also have properties like associative property, commutative property , and so on. There are six important properties of sets. Given, three sets A, B, and C, the properties for these sets are as follows.
Some important operations on sets include union, intersection, difference, the complement of a set, and the cartesian product of a set. A brief explanation of operations on sets is as follows. Set difference which is denoted by A - B, lists the elements in set A that are not present in set B. Set complement which is denoted by A', is the set of all elements in the universal set that are not present in set A.
The word well-defined refers to a specific property which makes it easy to identify whether the given object belongs to the set or not. For example: 1. The collection of children in class VII whose weight exceeds 35 kg represents a set. The collection of all the intelligent children in class VII does not represent a set because the word intelligent is vague. What may appear intelligent to one person may not appear the same to another person. Elements of Set:.
0コメント