Is a+b necessarily irrational?

[r0bHadz]

Homework Statement

If a is rational and b is irrational, is a+b necessarily irrational?

What if a and b are both irrational?

Homework Equations

The Attempt at a Solution

The books answer:

1)Yes, for if a+b were rational, then b = (a+b) - a would be rational.
This makes sense for me, but I looked at it a little differently:

If we have a number that never terminates after the decimal, and a number that does, or it keeps on repeating, then if we add those two the result will be a number that does not terminate.

2) If a and b are irrational, then a+b could be rational, for b could be r-a for some rational number a

This one confuses me. How can you say a is irrational, then go on to say that a is rational?

 

[r0bHadz]

Nvm I understand now, though his notation is pretty weird. Not sure why you would choose to use the same letter but whateva

 

[Mark44]

2) If a and b are irrational, then a+b could be rational, for b could be r-a for some rational number a

Nvm I understand now, though his notation is pretty weird. Not sure why you would choose to use the same letter

I'm certain it's a typo. The first sentence above should say "for b could be r - a for some rational number r."