- #1
lokisapocalypse
- 32
- 0
I need to show that a rational + irrational number is irrational. I am trying to do a proof by contradiction.
So far I have:
Suppose a rational, b irrational.
Then a = p/q for p, q in Z.
Then a + b = p/q + b = (p + qb) / q
But I don't know where to go from here because I still have a rational plus an irrational and that is what I am trying to show.
Also, would a similar proof work to show that an irrational + irrational = irrational?
So far I have:
Suppose a rational, b irrational.
Then a = p/q for p, q in Z.
Then a + b = p/q + b = (p + qb) / q
But I don't know where to go from here because I still have a rational plus an irrational and that is what I am trying to show.
Also, would a similar proof work to show that an irrational + irrational = irrational?