Yahoo Answers: Answers and Comments for Rational Plus Irrational? [Mathematics]
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From Blue Ridge
enUS
Fri, 02 Aug 2019 16:59:17 +0000
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Yahoo Answers: Answers and Comments for Rational Plus Irrational? [Mathematics]
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From JOHN: If u (rational) + β (irrational) = v (rationa...
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Fri, 02 Aug 2019 18:25:33 +0000
If u (rational) + β (irrational) = v (rational),
then u  v (rational) = β (irrational);
i.e., rational = irrational. Contradiction.
So u + β = γ (irrational),

From Math: Let's assume that the sum of the rational ...
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Sat, 03 Aug 2019 01:26:28 +0000
Let's assume that the sum of the rational number a/b (where a and b are integers) and irrational number x is also a rational number c/d (where c and d are some integer), i.e.
(a/b) + x = c/d
Then x = (c/d)  (a/b)
RHS is clearly rational while LHS is irrational. This is a contradiction.
Hence the sum must be irrational

From Pope: Suppose it is not true. In that case, let ther...
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Fri, 02 Aug 2019 17:21:51 +0000
Suppose it is not true. In that case, let there be a rational number r, and an irrational number x. Suppose their sum is rational, so this relation must be true:
r + x = a/b, for some certain integers a and b
Since r is rational, r = n/m, for some integers m and n.
r + x = a/b
m/n + x = a/b
x = a/b  m/n
x = (an  bm)/(bn)
But a, b, m, and n are all integers. Therefore, so are (an  bm) and bn. That means x is the ratio of two integers, which cannot be so for an irrational x. By contradiction, we must reject the proposition that r + x can be rational. Since the sum cannot be rational, it must be irrational.

From Mark: Because the irrational number can't be rep...
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Fri, 02 Aug 2019 17:06:13 +0000
Because the irrational number can't be represented by a fraction, so for instance, 4 + pi will be irrational, something like 7.14159(continue on into infinity).