Introduction
This course provides a brief review of introductory algebra topics. It includes some topics like Numbers (Real Number, Integer Number, Whole Number and so on…), Symbols and Series. Algebra is very wast topic in mathematics and used in daily life like measuring, calculating money, constructing build using measurement of length, height etc. Please find Video(s) as given below for more information.
Overview and Video
Numbers and Integers
- An integer is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 ⁄2, and √2 are not.
- Positive Integer are 1,2,3 …
- Negative Integer are -1,-6,-9, ….
- Number are any number like 1,2,3.300,5/2…..
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- There are many Types of Numbers in mathematics. They are explained in next slides.
- Set of Numbers like
{1,2,3,4….}
{0,1,2,…}
{2,4,6,8….}
{1/2,2/3,3/4,…}
Every set of number is having its own name feature.
The Natural Number
- The set of Number {1,2,3,4,5,….} is called as Natural number.
- It is denoted by N in the Mathematics world.
- Zero is not included in the Natural Numbers.
- Example –
N = {1,2,3,4,…..}
The Whole Numbers
- The set of Number {0,1,2,3,4,5,….} is called as Whole number.
- It is denoted by ‘W’ in the Mathematics world.
- Zero is special here in the set and it is making it as Whole Number.
- Examples:
W = {0,1,2,3,4,5,….}
Note: it is also called as Non-Negative Integers.
The Integers Numbers
- The set of Numbers which include positive and negative numbers along with zero is called Integer Number.
- It is super set of Natural Numbers and Whole Numbers and denoted as Z.
- Examples:
Z = {. . . ,−5,−4,−3,−2,−1, 0, 1, 2, 3, 4, 5, . . .}
- Positive Integers: Numbers right side of 0 is called as +ive integers.
- Negative Integer: Numbers left side of 0 is called as –ive integers.
- Absolute Number: If a is an integer, then the absolute value of a, written |a|, is defined as the distance between the integer and zero on the number line.
- Example: |-20| = 20, |-4|=4
The Rational Numbers
- Any number that can be written as a fraction is called a Rational Number.
- If “p” and “q” are integers (remember we talked about integers), then p/q is a rational number.
- Example: If p is 3 and q is 2, then: p/q = 3/2 = 1.5 is a rational number
- The only time this doesn’t work is when q is zero, because dividing by zero is undefined.
- Q={p/q : p and q are integers, q is not zero}
The Irrational Numbers
- The Number which are not rational is called irrational Number.
- The square root of 2 (√2) is an irrational number.
- The mathematical constant pi (π) is an irrational number that is much represented in popular culture. π=3.14159265358979
The Real Numbers
- Real Numbers include:
–The rational numbers, and
–The irrational numbers
- In fact a Real Number can be thought of as any point anywhere on the number line.
Real Numbers: {x : x is a rational or an irrational number}
Please download PPT from below link –