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Is the difference between two integers always smaller than either on of the numbers in the difference?
Yes
Which one is more irrational or rational?
You can choose an irrational number to be either greater or smaller than any given rational number. On the other hand, if you mean which set is greater: the set of irrational numbers is greater. The set of rational numbers is countable infinite (beth-0); the set of irrational numbers is uncountable infinite (more specifically, beth-1 - there are larger uncountable numbers as well).
Is the range for all quadratic functions the same as the domain?
No. The domain is usually the set of Real numbers whereas the range is a subset comprising Real numbers which are either all greater than or equal to a minimum value (or LE a maximum value).
Are imaginary numbers rational or irrational?
Imaginary numbers are not intrinsically rational or irrational.Of course, all real numbers are either rational or irrational numbers.Imaginary numbers are not real numbers.Imaginary numbers have a real part and an imaginary part, sometimes written like z=x+i y.The two parts, i.e. the x and the y, are real numbers. As real numbers, they are either rational or irrational. Its just that the two parts of a complex number may both be either rational or irrational or one may be rational and the other irrational. One could always make up a new name for these cases, but right now there is no such classification.
Is every whole number greater than one either prime or can be expressed as the sum of primes in exactly one way?
Yes it is called the fundamental theorem of arithmeticand it says that every whole number greater than one, the natural numbers, can be written as a unique product of primes. Dr. Chuck Mathdoc
