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Consider the numbers 1/3 , 7 , -15

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To which of these sets of numbers

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these numbers belong to. Lets review each of these

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Natural numbers are counting numbers

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not equal 0. it is 1,2,3,... so on and so forth

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The whole numbers are natural numbers plus 0

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Whole numbers are 0,1,2,3,4

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The integers is the whole numbers plus opposite of it

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It is whole numbers plus negative of natural numbers

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like -4,-3,-2,-1

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0, 1, 2, 3,4, ... so on and so forth

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rational numbers are numbers that can be expressed

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as a ratio of two integers.Rational number can be

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expressed as m/n where m and n are integers

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and n cannot be 0 as anything divided by 0

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is not defined. But m could be 0

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as 0 can be expressed as 0/1 or 0/2 or 0/3

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or 0/-537 these are all representations of 0

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Irrational numbers are numbers that cannot

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be expressed as ratios of integers

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examples of irrational numbers are numbers that

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keeps repeating on and on and on

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π, √2 are examples of irrational numbers

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and then real numbers are really all of these combined

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if you are combining the rational numbers

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and irrational numbers you are talking

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about real numbers.every real number

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is either rational or irrational.

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lets classify what we have

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1/3 is not a natural number as it is not

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a counting number. It is not a whole number

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it is not an integer.is it a rational number

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sure it is as 1 and 3 are integers. so 1/3

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is a rational number.if something is rational

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it cannot be irrational and it is also a real number

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lets try 7

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number 7 is a natural number, whole number

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any natural is a whole number

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any natural and whole number si an integer

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so 7 is also a integer.

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any number that is natural, whole and integer

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is a rational number. we can write 7 as 7/1

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we can write any integer as that number / 1

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if it is rational it cannot be irrational.

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it is also going to be real

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we have -15.

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it is not a natural number

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natural number are positive integers only

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it is not a whole number

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it is an integer, it is the opposite of +15

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it is rational as it can be written as -15/1

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and because it is rational it cannot be irrational

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it is also real.