Definition:Sufficiently Large

Definition

Let $P$ be a property.

We say that $P \left({x}\right)$ holds for all sufficiently large $x$ if:

$\exists a \in \R: \forall x \in \R: x \ge a: P \left({x}\right)$

That is:

There exists a real number $a$ such that for every (real) number not less than $a$, the property $P$ holds.

It is not necessarily the case, for a given property $P$ about which such a statement is made, that the value of $a$ is actually known, just that such a value exists.

Also see

• Arbitrarily Large