What is the sum of all irrational and rational numbers?
Will the resultant number be irrational or rational, Justify your answer?
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- "The sum of a rational number and an irrational number is irrational." By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats.
Why Is The Sum Rational And Irrational Number
- Each time they assume the sum is rational; however, upon rearranging the terms of their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.
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The sum of two irrational numbers is sometimes irrational. The sum of two irrational numbers, in some cases, will be irrational.
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