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Geometry/Counting Numbers


QUESTION: Hello sir

Sir before 3 or 4 weeks i asked a question to u .i.e why natural numbers are called whole numbers but whole numbers are not called naturals numbers.

So u replied---->

I assume by "whole number" you mean "integer".  If this is not the case, ask a follow-up and define "whole number."

Natural numbers are the numbers we use for counting: 1, 2, 3, ... (0 may or may not be included depending on the school of thought).

Integers include 0 and negative numbers: ..., -2, -1, 0, 1, 2, ...

Sir then to it is confusing for me that nutural is called whole  but why whole is not called natural.You have told natural numbers are counting numbers but whole numbers we cam't count.


ANSWER: Hi Aishwarya,

A very important concept to understand is that of subsets, which I will use to explain your issue below: "Sir then to it is confusing for me that nutural is called whole  but why whole is not called natural."

Let's use a somewhat silly example.  Suppose you like birds.  You can say "birds are animals".  That would be true.  However, would it be true to say "animals are birds"?  No, in general that is not true.  Although some animals are birds, not all animals are birds, therefore the statement is not true.  (You can put the word "all" at the beginning of the statement to make it easier to see if it is true.  "All birds are animals" : true.  "All animals are birds" : false.)
We say that birds are a subset of animals.  Or put another way, animals include birds.
Natural numbers are birds, and whole numbers are animals, and the metaphor is complete.  Understanding subsets is very important for the number system.

Now let's get to counting.  Imagine you're counting sheep.  You're probably going to use 1,2,3,...  You're not going to use negative numbers.  -1, -2, -3,... are whole numbers, but you won't use them for counting.  It is not the "natural" thing to do.  Hence the natural numbers are counting numbers, but the whole numbers are not.  Natural numbers are a subset of whole numbers.  All natural numbers are used for counting, but not all whole numbers are used for counting.

Hope this helps,

[an error occurred while processing this directive]---------- FOLLOW-UP ----------

QUESTION: Hello sir

Sir in last para slightly one confusion is there.We all know in number system natural, whole, integers, rational numbers, irrational numbers and all natural are whole and all whole are rational but all rational are not integers and all integers are not whole then why u said in eg of ship that -1,-2, -3 are whole numbers because -1,-2,-3 are integers but all integers are not whole number then why u said.

Sir are all rational numbers are Irational numbers.


Hi Aishwarya,

All integers are whole numbers.  If you disagree, please give me an example of an integer that is not a whole number.

Rational numbers are not irrational numbers.  There is no overlap.  If you take the union of rational numbers and irrational numbers, you get the real numbers.



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Azeem Hussain


I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.


4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

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Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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