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Help me to do this! I don't understand

Help me to do this! I don't understand-example-1

1 Answer

1 vote

Answer:

  1. {-6}
  2. N

Explanation:

You are given 6 numbers and asked to classify them with respect to the sets of Natural numbers, Integers, and Rational numbers.

The given numbers are ...

-6; 6,3; -0,1277; 6,(6); -6,073992...; 197

Here, the comma (,) is used as the decimal separator, and the parentheses (6) indicate a repeating digit.

Classification

The sets you're asked to use for classification are ...

  • ℕ — the set of natural numbers, {1, 2, 3, ...}
  • ℚ — the set of rational numbers
  • ℤ — the set of integers, {..., -3, -2, -1, 0, 1, 2, 3, ...}

(comma is used as a list separator)

Numbers

The numbers you're asked to classify are ...

  • -6; member of ℤ, but not ℕ
  • 6,3; member of ℚ, but not ℕ or ℤ
  • -0,1277; member of ℚ, but not ℕ or ℤ
  • 6,(6); member of ℚ, but not ℕ or ℤ
  • -6,073992...; not a member of ℚ, ℕ, or ℤ (irrational)
  • 197; member of ℕ and ℤ

Then the sets of interest are ...

1. (ℤ and not ℕ: negative integers) — {-6}

2. (ℕ and not ℚ: irrational counting numbers) — N, no such numbers

__

Additional comment

All natural number are integers, and all integers are rational numbers. Any member of ℕ or ℤ is a member of ℚ.

ℕ ⊂ ℤ

ℤ ⊂ ℚ

User Choldgraf
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