As we are heading towards making math easy to understand, so for taking one more step ahead here I’m today with a topic “NUMBER SYSTEMS” which is a very wide topic to be discussed over and to learn.
Before starting this topic I must tell you that this topic is the beginning of Abstract Mathematics.
so I’m going to start
Number System and Classification
Classification of numbers:-
the numbers (1,2,3,……∞) are classified into certain groups known as
- Natural Numbers
- Whole numbers
- Rational Numbers
- Irrational Numbers
- Real Numbers
- Complex Numbers
so here above mentioned groups are to give proper data to solve problems, now we are heading towards the brief description of each one
numbers from 1,2,3…… ∞ are known as natural numbers, it is also denoted as N.
whole numbers are actually Natural numbers but O is the number which makes this group as whole numbers i.e. 0,1,2,3…..
known as whole number set.
integers are the set of whole numbers and their additive inverses i.e.
this set is also represent by “I”.
The sum, difference of any integers are also integers.
Rational Numbers are those numbers which can be expressed as a ratio of two integers. for example: 2/5 , 5/50, -75/69.
All the integers included in the rational numbers.
All decimal expansions which terminates are rational numbers for example:-
and those decimal expansions which are having repeating patterns after some digits (as long as we don’t divide by multiples of 10) for example:-
20/3 = 0.66666…..
An Irrational numbers are that can be written as a ratio (i.e. p/q form q≠0) .
And its decimal expansions never ends ( non terminating) and also does not having repeating pattern ( non repeating).
the best example which I can give you for irrational Numbers is π(pi) = 22/7
π = 3.142857…….and so on
- Other famous irrational Number is golden ratio which has a great importance in Biology is (1+√5)/2= 1.618033….
the real numbers is the set of all rational and irrational Numbers. The real numbers are all the numbers which can be represented over number line i.e. Real Numbers are the set of Infinite numbers.
Complex Numbers are the set of a+ib
where i (iota)
is an imaginary unit a and b are real numbers. This group is used to represented by “C”.
for example:- x+ib ,5+i6 etc.
there are some rules for complex numbers I’m not going to reveal those in this article but don’t worry I’ll explain those some other day as I know I had explained numbers and their rules so I think that’s all enough for today,
Check the following image,
- which is explaining the whole concept explained above in a very approachable and tiny manner :-
except mentioned above Number system there are some other groups too like
Those numbers which are divisible by 1 or itself are known as Prime Numbers example:2,3,5,7,11,13,17…..
Pair of those numbers which are having 1 only as common factor are co prime Numbers Example: (3, 5)
though I had tried my best to explain Number System to a very approachable, even if you’re finding any doubt you can comment under the section.
Suggestions are appreciated.
Thank you for reading.