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# Why does the sum of rational number and irrational numbers are always irrational?

Wiki User

2014-03-06 00:11:38

Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.

Wiki User

2014-03-06 00:11:38
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