examples: 1, 2, 0, -5, sqrt(2), pi etc.
real numbers means numbers on the real plane.
the opposite of real numbers are imaginary numbers which takes the format of ai, in which the i is the imaginary unit
they do not exist on the real plane, but only on the imaginary plane. they can be found by square-rooting a negative number, e.g. sqrt(-4)=2i
usually imaginary numbers are used with real numbers, with the format a+bi, and this is called complex numbers.
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All irrational numbers are Real numbers - it's part of the definition of an irrational number. Imaginary numbers are neither rational nor irrational. An example of a number that is both Real and irrational is the square root of two. Another example is the number pi.
It means that when you exchange the two operands, the result doesn't change. Example 1: For any two real numbers, a + b = b + a. In the real numbes, addition is commutative. Example 2: For any two real numbers, ab = ba. In the real numbers, multiplication is commutative. Example 3: For square matrixes, AB is not the same as BA. Multiplication of matrixes is NOT commutative. Example 4: For vectors, a x b = - b x a. The cross product of vectors is NOT commutative.
No. For example, in real numbers, the square root of negative numbers are not defined.
real numbers
It is an equation which is insoluble in its domain. However, it may be soluble in a bigger domain.For example, x2 = 2 has no solution in the domain of rational numbers but it does in the real numbers, orx2 = -2 has no solution in the domain of real number but it does in imaginary numbers.