Natural number (counting number)

The most basic numbers used in algebra are those we use to count objects: \(1, 2, 3, 4, 5, …\) and so on. These are called the counting numbers also called natural numbers.

The notation “…” is called an ellipsis, which is another way to show “and so on”, or that the pattern continues endlessly. Natural numbers are an ordered succession, that is, they have an order in such a way as to establish (in ascending order) that each natural number that precedes another is less than the next (and obviously each number that follows is greater than the previous one). Therefore, for each natural number (excluding zero) always exists a previous number and the next one.

In practice 1 is less than 2, just as 2 is greater than 1 (so on for all numbers). The following mathematical symbols are used to indicate these relationships (and others):

  • \(<\) less-than
  • \(>\) greater-than
  • \(\leq\) less than or equal to
  • \(\geq\) greater than or equal to
  • \(=\) equal to
  • \(\neq\) not equal to
  • \(\ll\) much less than
  • \(\gg\) much greater than
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