It is uncountably infinite.
Yes, an infinite number of them.
Since there is an infinite number of real numbers and an infinite number of natural numbers, there is not more of one kind than of another.
A real number is a rational number that is not imaginary. 5, 3/4, and 8.6 are all real numbers. 3i is not a real number.
Infinitely rarely, a real number is also a rational number. (There are an infinite number of rational numbers, but there are a "much bigger infinity" of real numbers.)
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.
It is uncountably infinite.
Yes, an infinite number of them.
Since there is an infinite number of real numbers and an infinite number of natural numbers, there is not more of one kind than of another.
Infinitely rarely, a real number is also a rational number. (There are an infinite number of rational numbers, but there are a "much bigger infinity" of real numbers.)
A real number is a rational number that is not imaginary. 5, 3/4, and 8.6 are all real numbers. 3i is not a real number.
I sense you're talking about the infinite disk, the hyperbolic disk or the Poincare disk. The limit of the circumference is infinite and a real number and is not actually part of the hyperbolic plane.
There are an infinite number of real numbers that multiply to get 72.
Yes, unless it is an infinite, non-recurring number.
A natural number is a counting number, such as 1, 2, 3. There are also known as whole numbers and integers. They can be infinitely large. A real number is a number, possibly a natural number, but more possibly not, because there are an infinite number of real numbers that lie between any two natural numbers, such as 1, 1.1, 1.11, 1.111, 111112, etc, ad infinitum. Real numbers can also be infinitely large.
Infinity is not a number, it is an idea, or a concept. There are an infinite amount of numbers, but infinity is not one of them.
For any given subset, yes, because there are an infinite number of irrational numbers for each rational number. But for the set of ALL real numbers, both are infinite in number, even though the vast majority of real numbers would be irrational.