[catnaroek]

> something will only really be proven true when the probability hits 1

Careful. An event can have probability 1 even if its complement isn't empty: https://en.wikipedia.org/wiki/Almost_surely

[joshcohen]

In this setting we're using discrete probabilities so we don't have to worry:)

[tnecniv]

Good catch. The nuances of the continuum are many and subtle.