Prove that sum of a rational number and an irrational number is an irrational number.
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you can either prove it by contradiction
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Since the rational numbers are closed under addition, b=nm+(d−c) is a rational number. However, the assumptions said that b is irrational, and b cannot be both rational and irrational. This is our contradiction, so it must be the case that the sum of a rational and an irrational number is always irrational.
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