Whole numbers - what are they? Examples, definition

Whole numbers are positive integers and their opposite (-1, -2, -3, -4, -5), and the number zero. They are a generalization of the set of natural numbers into a set in which subtraction is workable. Importantly, the generalization of integers are rational numbers.

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1. Kinds of numbers

To make it easier to understand what integers are, let's first check what kinds of numbers we have.

  • Each number is a real number. For example: -5, 0, 3, π, √8.
  • Among the real numbers, we can indicate integers: -3, 0, 5 and natural numbers: 1, 2, 3, 4, 5 ...
  • Sometimes 0 is also a natural number.
  • We also have rational numbers, so those that can be written as a fraction, e.g. ½, ¾,.
  • Each integer is also a rational number because we can write it with a fraction, e.g. 5 = 5/1.
  • We also distinguish irrational numbers, i.e. roots: √9, √15, √27.
  • The roots that can be calculated are rational numbers, e.g .: √4 = 2, √9 = 3.
  • The irrational numbers, in turn, include π.
  • Rational and irrational numbers together form a set of real numbers.

2. What are whole numbers?

Whole numbers are an extension of natural numbers, so we include both natural and negative numbers, as well as the number zero. So integers are e.g., −10, −9, −8, −7, −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5 , 6, 7, 8, 9, 10.

In mathematics, we denote a set of integers with the symbol "Z" (from the German Zahlen - numbers) - and this designation is recommended by the Ministry of National Education. However, for ease of use, in most primary and secondary schools in Poland, we see the designation "C" for an integer - and such designation is not incorrect.

3. Whole numbers and natural numbers

Both natural and integer numbers can be added, multiplied and multiplied, with the certainty that the result of the action will be a natural number.

The set of positive integers is: Z = (1, 2, 3, 4, 5, 6, ...).

A set of negative integers: Z = (...− 6, −5, −4, −3, −2, −1).

To sum up - the set of positive integers is the set of natural numbers and their negative counterparts, as well as 0.

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