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List all the numbers from the given set that are, a.natural numbers b.whole numbers c.integers d.rational numbers, e.irrational numbers


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  1. a.natural numbers
    Numbers that are non-negative integers, such as 1,2,12,201,...
    There are two definitions of natural numbers, one that includes 0, and the other one does not. Most high-school definitions include 0.

    b.whole numbers
    Whole numbers do not have decimals nor fractions. They can be positive, negative, or zero. Examples are -100, -23, 0, 40, 47,1729,...

    Integers are whole numbers. This term is a more technical term than "whole numbers".

    d.rational numbers,
    Rational numbers are whole numbers or fractions that can be represented by division of two integers, m/n. Whole numbers can be represented by an integer divided by 1.
    Examples: 0, 3, 4/5, 144/17, 355/113, -45/13..., 0.4, 3.̅3 (=10/3),

    e.irrational numbers
    Irrational numbers are real numbers that are not rational, i.e. real numbers that cannot be represented as a quotient of two integers. Examples are: √2, -√94, π and e.

    This should give you a good idea of how to classify numbers. Proceed with the exercise and post your answers for checking if you wish.

    If you are wondering what a real number is:
    a real number is a number that is not complex. A complex number includes an imaginary component, i. A real number is a subset of complex numbers, which has the general form a+bi, where a and b are real numbers, and i is the square-root of -1. When b=0, the number becomes a real number.

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