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Are irrational numbers a part of the real number system?
Yes.
Why is a real number is a component of the real number system?
It would be a bit stupid to call a system the real number system if real numbers were not a part of it!
What is real about real numbers?
These numbers are real in contrast to complex numbers which contain an element which is called imaginary. All this arises because the square of any "normal" number is non-negative. So it is not possible to take the square root of a negative number. In some cases, though, there are mathematical advantages in being able to do so. So mathematicians introduce i, the square root of -1. Numbers involving i are said to be imaginary and, by way of contrast, those that don't, are said to be real. A number comprising a real part and an imaginary part is called a complex number.
What is it called if something is positive or negative?
Numbers that can be positive or negative include the integers, the rational numbers, the real numbers, and the complex numbers. All integers are rational numbers (numbers that can be written as a fraction, like 2/1), but most rational numbers are not integers -- like -1/2. (2/1, a rational, can be written as 2, an integer). The real numbers include all the rationals, plus many, many more numbers that can't be written as ratios or fractions, such as the square root of 2, pi, and the euler constant, e. As with the rational numbers and integers, there are as many negative real numbers as there are positive ones. Finally, we have the complex numbers. These include all of the real numbers, plus the roots of negative real numbers. Complex numbers are written in two parts -- a real part, plus an "imaginary" part (which is just as "real" as the real part, but is called "imaginary" for historical reasons). For example, 1 + i is a complex number with positive real and imaginary parts, while -1 - i is a complex number with negative real and imaginary parts. Positive and negative number systems are clearly very important in mathematics and in everyday life. They are all distinguished by the fact that they include magnitudes less than zero, as well as greater than zero (magnitudes of complex numbers are more complicated because complex numbers can have both positive and negative parts in one complex number!) There is also the term "non-zero" which refers to values that are positive or negative but not a value that is neither. It is a very important mathematical term since many functions (reciprocals, for example) can only have non-zero domains.
Is the zero imaginary number?
An imaginary number is a square root of a negative number. Imaginary numbers have the form bi where b is a non-zero (real number) and i is the imaginary unit, defined as the square root of − 1.if we define 'imaginary numbers' as 'complex numbers having a real part as 'zero' and a non-zero imaginary part'.. 0 doesn't fit in this description. But by, convention and for theoretical symmetry , we'll have to define 'real numbers' in pretty much the same way, and hence 0 would neither be a purely imaginary number or a purely real number.Overall i would say that 0 is a real number. Imaginary numbers only involve square roots of negative numbers.http://wiki.answers.com/Is_the_zero_imaginary_number#ixzz16w9viQWx
Are irrational numbers a part of the real number system?
Yes.
Why is a real number is a component of the real number system?
It would be a bit stupid to call a system the real number system if real numbers were not a part of it!
Are all whole numbers positive numbers?
Yes, EXCEPT for the number 0. It is a whole number but is not positive or negative. Real Numbers - Everything I. Rational Numbers- Any number except for non terminating decimals A. Integers- Any negative or positive number...not a decimal1. Whole Numbers- Any positive integer INCLUDING ZEROa. Natural Numbers- Any positive integer (NOT INCLUDING ZERO) The answer is not entirely correct, Whole numbers are numbers without a fractional part or decimal point. Therefore whole numbers can be negative as well as positive. -2 is a whole number but is not positive. There are a number of different interpretations for whole numbers, from non-negative integers, positive integers and all integers (which includes negative integers)
What are the sets of numbers that are part of the complex number system?
Real number set, imaginary number set, and their subsets.
Are positive numbers whole numbers?
No. Positive numbers can be whole numbers but they can also be decimal numbers and fractions. If a value is a whole number, it does not have a fraction or decimal part and it is not negative. Whole numbers are also called natural numbers or counting numbers.
Is -4 a imaginary number?
No, both positive and negative numbers are part of the so-called "real" numbers. The so-called "imaginary" numbers are outside the number line.Imagine the real numbers as a line from left to right, and the imaginary numbers a a separate line, from top to bottom. The place where they meet is zero. Positive is to the right of zero, negative to the left, imaginary numbers like +i or +3i to the top of zero, and negative imaginary numbes like -5i to the bottom of zero.
What is the smallest real number ever?
Real numbers are composed of rational and irrational numbers. Integers are part of the group (set) of rational numbers. And the integers are composed of the counting numbers (1, 2, 3, ...) and their negative counterparts (-1, -2, -3, ...). Oh, almost forgot. There is one more integer that is neither positive or negative. It's the number zero. Zero is an integer (neither positive or negative). The smallest real number ever is zero.
What real number is less than -1?
Many options - e.g. -2"Real number" means all the numbers we know, including positive and negative numbers.The only numbers that are not included are "imaginary numbers" - numbers that have an imaginary part i (used only i physics or high mathematics).See real-number
What is real about real numbers?
These numbers are real in contrast to complex numbers which contain an element which is called imaginary. All this arises because the square of any "normal" number is non-negative. So it is not possible to take the square root of a negative number. In some cases, though, there are mathematical advantages in being able to do so. So mathematicians introduce i, the square root of -1. Numbers involving i are said to be imaginary and, by way of contrast, those that don't, are said to be real. A number comprising a real part and an imaginary part is called a complex number.
Can a whole number be negative?
It seems to vary depending on who you ask. The definition of the set of whole numbers always includes the positive integers. However, it may also include zero and possibly the set of negative integers.
Is 24 a whole number?
No. In order to deliver 2.4 watermelons, you'd have to cut something up.
What number groups are irrational and rational numbers a part of?
Both are part of the real numbers.
