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# Why is the sum of an rational number and irrational number an irrational number?

Wiki User

2010-03-19 05:55:53

The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.

Wiki User

2010-03-19 05:55:53
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