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### Adding Rational and Irrational Numbers

```
Date: 11/09/1999 at 11:14:45
From: Jessica Troise
Subject: Abstract Math I

I was wondering how you could prove that a rational number added to an
irrational number results in an irrational number.
```

```
Date: 11/09/1999 at 12:54:15
From: Doctor Wilkinson
Subject: Re: Abstract Math I

When you want to prove something is irrational you should almost
always use an indirect proof. So suppose that x is rational and y is
irrational. You want to show that x + y is irrational, so you assume
it's rational. So you have

x          rational
y          irrational
x + y = z  rational

What happens if you solve

x + y = z

for y in terms of x and z?

- Doctor Wilkinson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
College Number Theory
High School Number Theory

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