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Answers:
natural numbers are counting numbers excluding zero, negatives and fractional numbers. (least broad)
whole numbers are natural numbers including zero but not negatives and fractional numbers. (2nd)
integers are whole numbers including zero and negatives but not fractional numbers. (3rd)
rational numbers are integers including zero, negatives and fractional numbers (terminating decimals). (4th)
irrational numbers are numbers that when expressed as a decimal, does not terminate, therefore cannot be written as a fraction. this is on the same level as fractional number, neither broader nor less broad. (4th)
real numbers include both rational and irrational numbers. (broadest)
Real numbers is the broadest.
Real numbers include both rational and irrational numbers.
Rational numbers include integers.
Integers include natural numbers.
Natural numbers = whole numbers.
However there is disagreement in the definition and some people might say that whole numbers (0, 1, 2, 3, ...) is the broader term than natural numbers (1, 2, 3, ...).
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