Download The Arithmetic of Numbers

Elementary Algebra Part I
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By: DHARMENDRA SAHU
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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Numbers and Integers Continue
• 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.
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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,…..}
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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.
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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, . . .}
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The Integers Numbers Continue..
• 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
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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}
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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
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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}
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The End
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