Answer:
- {-6}
- 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
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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