It cannot be. The cardinality of the set of real numbers is the Continuum. This is greater than the total number of sub-atomic particles in the universe!
No, the complement of real numbers is not a binary operation. A binary operation requires two elements from a set to produce a new element within the same set. The complement of the set of real numbers typically refers to elements not included in that set, which does not satisfy the criteria of producing a new element within the set of real numbers.
The complement of the set of real numbers, typically denoted as ( \mathbb{R}^c ), refers to all elements that are not included in the set of real numbers. In the context of the universal set being the complex numbers ( \mathbb{C} ), the complement would consist of all non-real complex numbers, which include imaginary numbers and numbers with non-zero imaginary parts. In general, the complement depends on the specified universal set in which the real numbers are being considered.
5 6356 5463 34 6 That is just not true. Real numbers do not include complex numbers, that is, those that include the square root of -1, for example.
Subtraction is definitely an operation defined on real numbers. I'm guessing you are actually asking why subtraction is not included as a commutative operation, this is because a-b is not always equal to b-a.
By its very name .. it is UNDEFINED. Even in the Extended Real Number set containing +-infinity these elements are UNDEFINED.
Rational numbers and Real Numbers. The multiplicative inverses of integers are not integers.
The grouping in which the numbers are taken does not affect the sum or product.
Real numbers include both positive and negative numbers, and also zero; also included are integers and fractions, including all types of fractions (rational, irrational, or transcendental). Only imaginary numbers are not real.
Infinite
It's a set with an infinite quantity of elements, like the set of all real numbers, or the set of all real numbers except zero, etc.
Yes. Anything that can be put on the number line is real. You will learn about imaginary and complex numbers in advanced math. They are included in complex numbers but again that is very advanced math.
The derived set of a set of rational numbers is the set of all limit points of the original set. In other words, it includes all real numbers that can be approached arbitrarily closely by elements of the set. Since the rational numbers are dense in the real numbers, the derived set of a set of rational numbers is the set of all real numbers.