- #1

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**Is there an easy way to prove....**

that a rational number + an irrational number is either rational or irrational?

Just pick 2 elements and show that it the sum is rational and irrational?

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- Thread starter tronter
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- #1

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that a rational number + an irrational number is either rational or irrational?

Just pick 2 elements and show that it the sum is rational and irrational?

- #2

cristo

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that a rational number + an irrational number is either rational or irrational?

Just pick 2 elements and show that it the sum is rational and irrational?

That's not a proof, as I explained to you before. A proof must hold true for ALL values, not just one or two.

You need to show some work in the HW forum. What have you tried?

- #3

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Let [tex] x = \frac{p}{q} [/tex] and [tex] y [/tex] be an irrational number. Then show that this sum leads to a form [tex] p/q [/tex] or that it cannot be expressed in that form?

Or do a contradiction (e.g. assume that it is neither irrational nor rational)?

- #4

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that a rational number + an irrational number is either rational or irrational?

- #5

HallsofIvy

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Of course, if m is rational and x is irrational, then x+ m= n with n rational leads immediately to x= m-n, a contradiction.

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