To provide a precise response, I need to know more about which specific number sets you are comparing (e.g., natural numbers, whole numbers, integers, rational numbers, real numbers, complex numbers, etc.). Each of these sets has specific relationships and properties.
Here are some general statements that are often true regarding these common number sets:
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Natural Numbers (N) ⊆ Whole Numbers (W): The set of natural numbers (1, 2, 3, ...) is a subset of whole numbers, which include zero (0, 1, 2, 3, ...).
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Whole Numbers (W) ⊆ Integers (Z): The set of whole numbers is a subset of integers, which include negative numbers as well (…, -3, -2, -1, 0, 1, 2, 3, ...).
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Integers (Z) ⊆ Rational Numbers (Q): Every integer can be expressed as a rational number (e.g., 2 can be written as 2/1).
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Rational Numbers (Q) ⊆ Real Numbers (R): The set of rational numbers, which includes numbers that can be expressed as the quotient of two integers, is a subset of real numbers, which also includes irrational numbers.
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Real Numbers (R) ⊆ Complex Numbers (C): Every real number can be considered a complex number with an imaginary part of zero (e.g., the number 3 can be expressed as 3 + 0i).
If you have specific sets or statements in mind, please let me know!