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all integers, positive and negative and zero;

all fractions, positive and negative, including mixed numbers, which of course can be written as improper fractions -- this is the same as saying all numbers which can be written as terminating or recurring decimals;

all other numbers which can be represented as infinite, non-recurring decimals.

e.g. pi = 3.14159265 ... continues indefinitely, and never settles down to a repeating pattern. Computers have calculated it to thousands of decimal places.

so all integers are also icluded in real numbers