summary
Completion requirements
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Natural Numbers (ℕ): {1, 2, 3, 4, …}
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Used for counting.
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Closed under addition and multiplication.
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Integers (ℤ): {…, -3, -2, -1, 0, 1, 2, 3, …}
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Extends natural numbers by including zero and negative numbers.
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Allows subtraction.
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Rational Numbers (ℚ): {a/b | a, b are integers, b ≠ 0}
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Includes fractions and whole numbers.
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Allows division (except by zero).
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Irrational Numbers: {√2, π, e, …}
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Cannot be written as a fraction (a/b form).
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Decimal representation is non-repeating and non-terminating.
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Real Numbers (ℝ):
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Includes both rational and irrational numbers.
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Represents all points on a number line.
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