It is a number we require for measuring rather than counting. Hence a real number is any rational or irrational number that we might name. They are the numbers we expect to find on the number line.
An irrational number can result only from a theoretical calculation; examples are the Pythagorean theorem, and solving
an equation such as x³ = 5.
Any serious theory of measurement must address the question: Which irrational numbers are theoretically possible? Which ones could be actually predictive of a measurement?)
3 Real, rational, integer. | −3 Real, rational, integer. | |
−½ Real, rational. | Real, irrational. | |
5¾ Real, rational. | − 11/2 Real, rational. | |
1.732 Real, rational. | 6.920920920. . . Real, rational. | |
6.9205729744. . . Real. And let us assume that it is irrational, that is, that the digits do not repeat. Moreover, we must assume that there is an effective procedure for computing each next digit. For if there were not, then we would not know which number we are computing. And that symbol would not refer to any "number"! | ||
6.9205729744 Real, rational. Every exact decimal is rational. |
A real variable takes on values that are real numbers.
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