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Geometry/Definitions in the Number System


Hello sir

Sir natural numbers means -- All counting numbers are called natural numbers

Whole numbers---All counting numbers included 0 are called whole numbers.

Integers--All whole numbers with negative and positive sign are called integers

Rational numbers--- P and q are integers in the form of fraction and if q is not equal to 0 are called rational numbers.

Irrational numbers---- The numbers which cannot be expressed in the form of p/q .
Real numbers---- The set of rational and irrational are called real numbers.
For me these are confusing, sir i provided the difinations.
My confusion is are ntural numbers are different nad whole numbers are different. If so when we use numbers in our day to day life , which we will use, from natural or whole.

Sir i wnat to clarify that natural numbers are the only numbers which the mathmaticins have named as natural.But sir numbers were there sir, so they can name from whole, why they named as natural, already numbers were with them , to use the numbers in maths operations, they can name then from whole, why they named from natural.

Sir how whole numbers can be integers, whole numbers only different and integers only different.


Hi Aishwarya,

Thank you for providing these definitions.  It is important to know them, to understand them, and to have them memorized.  It is also important to accept them.  Although in your opinion it may be a silly or otherwise bad definition, you must accept it, as this is the terminology that is standard.  You can't open up a dictionary and argue with what you find.

Natural numbers are 1,2,3,...
Whole numbers are 0,1,2,3,...

Based on the definitions you provided, whole numbers are all the natural numbers, and zero.  The only difference between the natural and whole numbers is that whole numbers include zero.  (I actually have not seen "Whole numbers" defined this way before.  "Natural plus zero" is what I would see instead.)  These sets of numbers overlap.  I don't know what numbers you use in your day-to-day life.  Suppose you use, 4, 5, and 6.  These are included in the natural numbers.  They are also included in the whole numbers, the rationals, and the reals.  I don't understand why you would "stop and think" about which set the numbers belong to.

I don't understand what you mean about mathematicians naming numbers as natural.  Once again, do not argue with the definitions.

Integers are ...,-3,-2,-1,0,1,2,3,...

So all the whole numbers AND the negative versions of the whole numbers.

Hope this helps,


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Azeem Hussain


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