The Pessimist Sentences

Logic Level 2

For every \(n \geq 1\), there is an \(n^\text{th}\) Pessimist sentence saying that not all later Pessimist sentences are true. For example, the \(5^\text{th}\) Pessimist sentence says:

"For at least one \(m > 5\), the \(m^\text{th}\) Pessimist sentence is false."

Where \(t\) and \(f\) are the number of true and false Pessimist sentences, what is \(t+f\)?

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