ITE04: DISCRETE MATHEMATICS
What is Discrete Mathematics?
Discrete mathematics is a study that focuses on
countable, distinct, and separate objects or structures. It
deals with mathematical concepts and structures that do
not involve continuous values but rather discrete
elements. (non-continuous data)
DISCRETE VS. CONTINUOUS
Discrete
• Finite value that can be counted
• Discrete things are separate and distinct, like
counting whole numbers (1, 2, 3, ...).
• You can't have values in between, like 1.5 or 2.75.
• Examples include the number of students in a
classroom, the count of apples on a tree, or the
results of rolling a die (1, 2, 3, 4, 5, or 6).
Continuous
• Infinite value that can be measured
• Continuous things flow smoothly and can take on
any value within a range.
• You can have values in between, like 1.5 or 2.75.
• Examples include time, temperature, and height.
You can have any time, any temperature, or any
height within a certain range.
SETS OF NUMBERS
Natural Numbers (N):
• Natural numbers are positive whole numbers,
starting from 1 and going infinitely.
• Examples: 1, 2, 3, 4, 5, ...
Whole Numbers (W):
• Whole numbers include all natural numbers along
with zero.
• Examples: 0, 1, 2, 3, 4, 5, ...
Integers (Z):
• Integers include all positive and negative whole
numbers along with zero.
• Examples: -3, -2, -1, 0, 1, 2, 3, ...
Rational Numbers (Q):
• Rational numbers are numbers that can be
expressed as a fraction, where the numerator and
denominator are integers, and the denominator is
not zero.
• Examples: 1/2, -3/4, 7 (can be written as 7/1),
0.25 (can be written as 1/4).
Real Numbers (R):
• Real numbers include all rational numbers and all
irrational numbers.
• Examples: 3.14 (π, an irrational number), √2 (also
an irrational number), 5 (a rational number), -1/3
(a rational number).
Complex Numbers (C):
• Complex numbers are numbers in the form a + bi,
where "a" and "b" are real numbers, and "i"
represents the imaginary unit (i = √(-1)).
• Examples: 3 + 2i, -1 - 4i, 5 (a complex number
with no imaginary part is still a complex number).
Prime Numbers
• A prime number is a natural number greater than
1 that has exactly two distinct positive divisors: 1
and itself. In other words, a prime number can
only be divided by 1 and itself without leaving a
remainder.
• Examples: 2: The smallest prime number, 3:
Another small prime number, 5: Yet another
example of a prime number, 7: A prime number
that can only be divided by 1 and 7.
