Q: Is the difference between two real numbers a real number?

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Integer numbers are a subset of real numbers. Real numbers may contain fractions.

No difference. The set of complex numbers includes the set of imaginary numbers.

The graph of imaginary numbers takes two axes. A part for the real part and the i part.

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.

Graphically the difference is quite clear: the real numbers can be put on a line, the so-called number-line; while complex numbers are represented as points on a plane. A complex number is made up of two parts, like a vector in two dimensions.

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Rational numbers are numbers that can be written as a fraction. Real numbers are any number, including irrationals.

Integer numbers are a subset of real numbers. Real numbers may contain fractions.

The set of real numbers is a subset of the set of complex numbers. For the set of complex numbers, given in the form (a + bi), where a and b can be any real number, the number is only a real number, if b = 0.

No. 5 and 2 are real numbers. Their difference, 3, is a rational number.

If you are talking about integers on the number line, the answer is 1. If you are talking about real numbers, then there is always a real number between every other two, so you can't really talk about the difference.

No difference. The set of complex numbers includes the set of imaginary numbers.

The graph of imaginary numbers takes two axes. A part for the real part and the i part.

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.

The sum or the difference between two irrational numbers could either be rational or irrational, however, it should be a real number.

A complex number is any number that is in the real/imaginary plane; this includes pure reals and pure imaginaries. The difference between two numbers inside this plane is never outside this plane; therefore, yes, the difference between two complex numbers is always a complex number. However, the difference between two numbers that are neither purely imaginary nor purely real is not always necessarily a number that is neither purely imaginary nor purely real. Take x+yi and z+yi for instance, where x, y, and z are all real: (x+yi)-(z+yi)=x+yi-z-yi=x-z. Since x and z are both real numbers, x-z is a real number.

Graphically the difference is quite clear: the real numbers can be put on a line, the so-called number-line; while complex numbers are represented as points on a plane. A complex number is made up of two parts, like a vector in two dimensions.

Rational numbers form a proper subset of real numbers. So all rational numbers are real numbers but all real numbers are not rational.