Nope not all the rational functions have a horizontal asymptote
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No. For example, in real numbers, the square root of negative numbers are not defined.
No because all integers are rational numbers
Yes. Every integer is a rational number. Every rational number is a real number. Every real number is a complex number. The complex numbers include all real numbers and all real numbers multiplied by the imaginary number i=sqrt(-1) and all the sums of these.
Not at all. Every whole number is rational.
Numbers are split into real and imaginary. Rational numbers are under the category: Real. Therefore all rational numbers are real. An irrational number is also real, but can not be expressed as a fraction.