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Natural Numbers

• Definition: The set of natural numbers includes all positive integers, starting from one.

• Characteristics:

  • Does not include fractions or decimals.

  • The smallest natural number is 1.

  • The set is infinite, indicating there is no limit to the number of elements.

• Abbreviation:

  • Can be abbreviated as:

  • N = {1, 2, 3, \ldots, \infty}

Whole Numbers

• Definition: The set of whole numbers includes all elements in the set of natural numbers plus one additional element, which is zero.

• Characteristics:

  • Contains all positive integers and zero.

  • Does not include fractions or decimals.

  • The set is infinite, with no limit to the number of elements.

• Abbreviation:

  • Can be abbreviated as:

  • W = {0, 1, 2, 3, \ldots, \infty}

Relationship Between Natural Numbers and Whole Numbers

• Natural numbers are a subset of whole numbers.

Integers

• Definition: The set of integers includes all positive numbers, negative numbers, and zero.

• Characteristics:

  • Does not include fractions or decimals.

  • The set is infinite, indicating no limit to the number of elements.

• Abbreviation:

  • Can be abbreviated as:

  • Z = {\ldots, -2, -1, 0, 1, 2, \ldots}

Relationship Between Integer Sets

• Natural numbers and whole numbers are both subsets of integers.

• The set of integers encompasses both positive and negative whole numbers along with zero, indicating a broader range than natural and whole number sets.