# Thread: Proof Dealing with real and rational numbers

1. ## Proof Dealing with real and rational numbers

I'm having trouble understanding how to prove this problem. I need some help.

Let a ∈ ℚ, a ≠ 0 and b ∈ ℝ \ ℚ. Prove the following:
a) a + b ∈ ℝ \ ℚ
b) ab ∈ ℝ \ ℚ
c)1/b ∈ ℝ \ ℚ

Thanks for any help provided

2. Originally Posted by tuyt6444
I'm having trouble understanding how to prove this problem. I need some help.

Let a ∈ ℚ, a ≠ 0 and b ∈ ℝ \ ℚ. Prove the following:
a) a + b ∈ ℝ \ ℚ
b) ab ∈ ℝ \ ℚ
c)1/b ∈ ℝ \ ℚ

Thanks for any help provided

All you have to know is that the rational numbers $\mathbb{Q}$ is a field: closed under sum, multiplication and inverses (for elements different from zero, of course).

Tonio