# 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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