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# What is a non-real number?

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A non-real, or imaginary, number is any number that, when multiplied by itself, produces a negative number. Mathematicians use the letter "i" to symbolize the square root of -1. An imaginary number is any real number multiplied by i. For example, 5i is imaginary; the square of 5i is -25.

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No real negative number can have a negative square root, because even a negative number multiplied by itself produces a positive product. Real numbers are those numbers that represent a quantity along a number line, including all positive and negative numbers and zero. Irrational numbers, even though they cannot be expressed as a precise fraction or decimal, are considered real numbers because they do exist at some place on the number line, even if that place is not precisely defined.

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## Related Questions

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Non-integers include fractions, decimal numbers and imaginary numbers. In math, integers include the set of all the counting numbers, their inverses or negatives, and zero, leaving all other numbers as non-integers. There are an infinite number of non-integers, just as there is an infinite number of integers.

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Every point on a number line corresponds to a unique real number. A line is an infinite set of points and the set of real numbers is also infinite. Thus, there exists a one-to-one correspondence between the set of real numbers and the points on a number line.

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Pi is a real number, as all numbers that exist on a number line are real. Real numbers include all rational and irrational numbers; pi is defined as an irrational number.