Introduction:
Relationships between two objects are represents as a set of ordered pairs of objects, the concept of ordered pair is defined using sets, natural numbers, which are the basis of other numbers, are also defined using sets.This concept of the function being a special type of relation, is based on sets, and graphs and digraphs consisting of lines and points are described as an ordered pair of sets. I like to share this Factor Numbers with you all through my article.
Concepts of set of numbers:
The followings are some of the concepts of set of numbers.
Empty set or Null Set or Void set:
A set which contains no element is called the empty or null or void set. It is denoted by the symbol Ø. Thus Ø = { }. We observe that n(Ø) = 0.
Equivalent sets:
If two sets that can be contains the same elements are called as the equivalent sets .If the set A is equivalent to the set B, then n(A) = n(B) and we write A ? B.
Singleton set:
A set has only one element is called a singleton set.
Universal Set:
The elements of all sets that can be occur in the mathematical investigations belong with a set. This set is called the universal set. The universal set is denoted by the symbol U or by the symbol E.We can study the universal set by its conception. I have recently faced lot of problem while learning An Odd Number, But thank to online resources of math which helped me to learn myself easily on net.
Examples for set of numbers:
Example: 1
• Given the set of numbers [7, 14, 21, 28, 35, 42], find a subset of these numbers that sums to 100.
• First, make sure you understand the terminology: "...sums to 100" means that the object is to locate some grouping of the numbers in the original set that, when added together, add up to 100. You might expend all day on this seemingly simple question before giving up in frustration.
• Before you even try adding together some of these numbers together, in hopes of stumbling on the answer, take a look at the numbers themselves.
• They are all multiples of 7, which means that they be able to each be represented as a digit times 7. Or, since multiplication is really just a shortened form of adding up, they can each be represented by a group of 7s being added together:
• Now notice what happens when you attempt adding up these numbers together. let say you add 21 and 28:
• 7 = 7 x 1 = 7
• 14 = 7 x 2 = 7 + 7
• 21 = 7 x 3 = 7 + 7 + 7
• 28 = 7 x 4 = 7 + 7 + 7 + 7
• 35 = 7 x 5 = 7 + 7 + 7 + 7 + 7
• 42 = 7 x 6 = 7 + 7 + 7 + 7 + 7 + 7
21 + 28 = (7 x 3) + (7 x 4) or (7 + 7 + 7) + (7 + 7 + 7 + 7)
• The associative belongings of addition states that the combination of elements doesn't make a difference; you can simply remove the parentheses when only addition is involved, which gives you this:
21 + 28 = 7 + 7 + 7 + 7 + 7 + 7 + 7 or 7 x 7
• Looking back at the original problem, it is now clear that it's a trick question. because you start with all multiples of 7, there cannot be a subset of those numbers that sums to 100 because 100 is not a multiple of 7. The closest you can get is either 98 (42 + 35 + 21) or 105 (42 + 35 + 28).
Example: 2
Consider a set A = {-1 ,0,1} It is a non empty set, the elements are -1,0,1. Perform the action of multiplication on this set taking two elements at a time.
Solution:
All the possible ways of takes two elements and find their product is given below
-1 x 0 = 0
-1 x 1 = -1 Observe the products belong to the set A
1 x 1 = 1 Under such a order we say that A is closed under
-1 x -1 = 1 multiplication operation.
1 x 0 = 0
0 x 0 = 0
This property is called Closure property with esteem to Multiplication operation.
Relationships between two objects are represents as a set of ordered pairs of objects, the concept of ordered pair is defined using sets, natural numbers, which are the basis of other numbers, are also defined using sets.This concept of the function being a special type of relation, is based on sets, and graphs and digraphs consisting of lines and points are described as an ordered pair of sets. I like to share this Factor Numbers with you all through my article.
Concepts of set of numbers:
The followings are some of the concepts of set of numbers.
Empty set or Null Set or Void set:
A set which contains no element is called the empty or null or void set. It is denoted by the symbol Ø. Thus Ø = { }. We observe that n(Ø) = 0.
Equivalent sets:
If two sets that can be contains the same elements are called as the equivalent sets .If the set A is equivalent to the set B, then n(A) = n(B) and we write A ? B.
Singleton set:
A set has only one element is called a singleton set.
Universal Set:
The elements of all sets that can be occur in the mathematical investigations belong with a set. This set is called the universal set. The universal set is denoted by the symbol U or by the symbol E.We can study the universal set by its conception. I have recently faced lot of problem while learning An Odd Number, But thank to online resources of math which helped me to learn myself easily on net.
Examples for set of numbers:
Example: 1
• Given the set of numbers [7, 14, 21, 28, 35, 42], find a subset of these numbers that sums to 100.
• First, make sure you understand the terminology: "...sums to 100" means that the object is to locate some grouping of the numbers in the original set that, when added together, add up to 100. You might expend all day on this seemingly simple question before giving up in frustration.
• Before you even try adding together some of these numbers together, in hopes of stumbling on the answer, take a look at the numbers themselves.
• They are all multiples of 7, which means that they be able to each be represented as a digit times 7. Or, since multiplication is really just a shortened form of adding up, they can each be represented by a group of 7s being added together:
• Now notice what happens when you attempt adding up these numbers together. let say you add 21 and 28:
• 7 = 7 x 1 = 7
• 14 = 7 x 2 = 7 + 7
• 21 = 7 x 3 = 7 + 7 + 7
• 28 = 7 x 4 = 7 + 7 + 7 + 7
• 35 = 7 x 5 = 7 + 7 + 7 + 7 + 7
• 42 = 7 x 6 = 7 + 7 + 7 + 7 + 7 + 7
21 + 28 = (7 x 3) + (7 x 4) or (7 + 7 + 7) + (7 + 7 + 7 + 7)
• The associative belongings of addition states that the combination of elements doesn't make a difference; you can simply remove the parentheses when only addition is involved, which gives you this:
21 + 28 = 7 + 7 + 7 + 7 + 7 + 7 + 7 or 7 x 7
• Looking back at the original problem, it is now clear that it's a trick question. because you start with all multiples of 7, there cannot be a subset of those numbers that sums to 100 because 100 is not a multiple of 7. The closest you can get is either 98 (42 + 35 + 21) or 105 (42 + 35 + 28).
Example: 2
Consider a set A = {-1 ,0,1} It is a non empty set, the elements are -1,0,1. Perform the action of multiplication on this set taking two elements at a time.
Solution:
All the possible ways of takes two elements and find their product is given below
-1 x 0 = 0
-1 x 1 = -1 Observe the products belong to the set A
1 x 1 = 1 Under such a order we say that A is closed under
-1 x -1 = 1 multiplication operation.
1 x 0 = 0
0 x 0 = 0
This property is called Closure property with esteem to Multiplication operation.
