Classification of numbers
The chart below will help you with the classification of numbers a lot. It will makes things crystal clear.
Important observations you need to make from the chart.
Observation #1:
Notice that √(9) is a natural number. It is because √(9) = 3
Observation #2:
Notice that the only difference between natural numbers and whole numbers is the zero.
Whole numbers = Natural numbers + zero
Observation #3:
Notice that the difference between whole numbers and integers are the negative numbers.
Integers = Whole numbers + the negative of the whole numbers
Observation #4:
All integers are fractions. Not all fractions are integers
Example: 2 is an integer and can be written as 2/1 to make it a fraction.
However, 1/3 = 0.333333333 is not an integer
Observation #5:
Fractions can be written as a terminating decimal or a repeating decimal
Example: 1/2 = 0.5 and 0.5 is a terminating decimal. 1/3 = 0.3333333 and 0.3333333 is a repeating decimal
Observation #6:
Rational numbers = Integers + fractions
Observation #7:
Irrational numbers are numbers that cannot be written as a fraction
Example: pi= 3.14..., 2.224879566117426874, √(7)
Another way to see them is that they are neither repeating decimals nor terminating decimals
Observation #8:
Real numbers = rational numbers + irrational numbers
Observation #9:
The difference between complex numbers and real numbers is that complex numbers give solutions for the following expressions and more!
√(7), √(18), √(25) = 5i, etc...
Among the different types of numbers, fractions is among the toughest to understand
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Feb 17, 19 12:04 PM
There is no rational number whose square is 2. An easy to follow proof by contraction.
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