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All numbers in the physical world are (positive) real numbers.

Real numbers are all numbers from minus infinity to plus infinity.

Integers are real (rational) numbers with a fractional (decimal part) value of zero or, with no fractional or decimal part.

Real numbers are divided in to rational numbers and irrational numbers.  Irrational numbers cannot be expressed as a ratio of  p / q, where p and q are integers.

Rational numbers are further divided in to fractions and whole numbers or integers.

Examples of integers are  -21324,  -4 , 0 , +1, +838383

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