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Geometry/Real Numbers and Inclusion

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Question
Hello sir

Sir if all natural, whole, integers, rational,irrational no's are called real no's then we can use the word directly as real no's why we should use different.

Answer
Hi Aishwarya,

Naturals, integers, rationals, and irrationals are all subsets of real numbers.  This means there exists a real number that is not a natural number, a real number that is not an integer, and so on.

Let me try to explain this concept of inclusion in a different way.  We have peppers, fruits, vegetables, and food.  Would it be good to only use the word "food"?  Although you could, it helps to have the different categories because that helps you refer to different sets with similar properties.  Some foods have seeds, but without naming the category "fruit", we cannot quickly refer to all these specific foods.
In this example, real numbers are like food, and the other sets of numbers are the more specific types of foods.

Hope this helps,
Azeem

Geometry

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Azeem Hussain

Expertise

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

Experience

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

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
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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