I am self studying measure theory from Sheldon Axler's book Measure, Integration & Real Analysis. In page 21 (2.18) the author presents the non additivity of Outer Measure as:
There exist disjoint sets $A$ and $B$ of $\mathbb{R}$ such that: $$\left |A\cup B \right | \neq \left |A\right |+ \left|B\right |$$
In the follow up to this, earlier the author has proven easily the property of countable subadditivity of outer measure (2.8).
Suppose $A_{1},A_{2},...$ is a sequence of subsets of $\mathbb{R}$, then:
$$\left | \bigcup_{k=1}^{\infty }A_{k}\right | \leq \sum_{k=1}^{\infty}\left | A_{k} \right |$$
My question is - isn't 2.18 - i.e. Non Additivity of Outer Measure, is a corollary of property 2.8?