No. Numbers are abstract concepts: they are alive and so have no feelings (sorry, numbers!)
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Adding two negative numbers will always be negative. Subtracting two negative numbers may be positive or negative. Dividing or multiplying two negative numbers will always be positive.No
Yes. "Integer" includes positive numbers, negative numbers, and zero.
Whole numbers are RATIONAL. That includes negative whole numbers.
Of the "standard sets" -10 belongs to: ℤ⁻ (the negative integers) ℤ (the integers) ℚ⁻ (the negative rational numbers) ℚ (the rational numbers) ℝ⁻ (the negative real numbers) ℝ (the real numbers) ℂ (the complex numbers) (as ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ). Other sets are possible, eg the even numbers.