What does "overwhelming" mean in cryptography?

Question

I found the term "overwhelming" when I study cryptography.

According to the definition, we call $f$ overwhelming if $1-f$ is negligible.

I already know the negligible function and its way to use but I don't understand why we consider the overwhelming function.
Can someone teach me how to use it and some examples?

Answer 1

"With overwhelming probability" means that an event happens with probability at least $1−2^{Ω(n^\varepsilon)}$ for a constant $\varepsilon >0$.

Example: In a public key cryptosystem where $\mathcal{PK}$, $\mathcal{SK}$ and $\mathcal{R}$ are the spaces of public keys, secret keys, and sender randomness respectively, if $∆_{\mathcal{R}}$ denote the distribution on $\mathcal{R}$, then we require the usual correctness condition: for all $pk ∈ \mathcal{PK}$, all $sk ∈ \mathcal{SK}$, and $b ∈ \{0, 1\}$, we have $Dec_{sk}(Enc_{pk}(b; r)) = b$ with overwhelming probability over $r ← ∆_{\mathcal{R}}$.