Saturday, April 18, 2009

Real Numbers

If we combine the rational numbers with the irrational numbers we get the real numbers. In the real numbers we find positive numbers, negative numbers, integers, fractions, square roots, cube roots, fractional roots, π, e, zero...

Like the rational numbers, we can add, subtract, multiply and divide any two numbers (except dividing by zero). But with the real numbers we can also raise any positive number to the power of any other number. We can now do fractional powers and get a real answer because the irrationals are part of the reals. However, we cannot raise negative numbers to every fraction. (-1)(1/2) = √(-1) is not allowed with the real numbers, although (-1)(1/3) is allowed because it equals -1.

The real numbers are given the symbol: ℝ

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