In Borges' story The Immortal, he writes "They knew that in an infinite period of time all things happen to all men."
This is quite a commonly heard thought: of all things happening within infinity. However the logic doesn't really hold. In an infinite temporal framework there is absolutely no reason I am fated to, for example, cut off my left leg and use it as a tool in a variation of hockey played in the sewers of Rotterdam involving an opposition of asthmatic lepers. Borges is confusing two separate things; time and events. An example of this absurdity being that within his infinity notion, I am also fated to hop a marathon on my left leg, though my left leg is no longer present. But it is an event within the infinity of events. Therefore it must happen. Not, however, if it can't.
Something not happening today, like the leg hockey situation, is in no sense an argument why it should happen tomorrow, or within an infinity of tomorrows. An immortal could simply spend infinity sitting in a cave.
Borges later writes: "If we postulate an infinite period of time with infinite circumstances and changes, the impossible thing is not to compose the Odyssey, at least once."
This second quote is perfectly logical however: that within a universe of infinite circumstances all circumstances one could mention must be contained. However, it is logic simply because it is an exercise in tautology. Of course, if we conjecture a universe of infinite circumstances, then all possible circumstances must be contained within such a universe. That is the nature, the internal logic of the sentence. But this is simply an imposed intellectual framework, the closed system of a thought-piece.
On the other hand, there is no possible reason all possible events must occur within infinite time. It is an unjustified inference; a confusion of the finite with the infinite. This understanding of infinity is merely the finite extended or pushed to a higher power. A mind pushing itself and its boundaries to its limits, but still contained within those limits, and producing absurdities when it imbues those limits with limitlessness, or infinity. The infinite is a beast not so easily captured.
The danger of the joys of abstract thought where one's errors are not demonstrated in reality, though Borges might argue that his is a work of art, and such flaws are cracks within which further creative thought grows. Though that's no excuse.