$\omega \subseteq \mathbb{R}^+$ is called a Sidon sequence, if all the sums $a + a' \ (a, a' \in \omega, a \leq a')$ are distinct, and it is an asymototic basis of order $2$, if any positive integer $n$ sufficiently large can be expressed as a sum of $2$ elements of $\omega$.

According to the article I am reading, apparently it is not too difficult to show that there does not exist $\omega$ such that it is a Sidon sequence and also an asymototic basis of order $2$, but I am not quite seeing how to prove this at the moment.

I was wondering if someone could possibly give me an explanation on how to show this? Thank you very much!