A reformulated comparison method that assigns lexical or hyperreal values to infinite prospects still cannot escape the result that infinitely many mixed strategies remain rationally equivalent to pure belief.

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Hyperreal values(as used in mathematical logic and decision theory): Numbers that go beyond regular infinity in a mathematical way, allowing for infinitely small and infinitely large quantities to be compared precisely.
Infinite prospects(as used in decision theory): Possible outcomes or scenarios that are endless in number—so many possibilities that you could never finish listing them all.
Lexical values(as used in decision theory and comparisons): A way of ranking or ordering things in a strict priority list, where the first item always matters most, then the second, and so on—like how a dictionary organizes words alphabetically.
Mixed strategies(as used in game theory and rational decision-making): A plan where you randomly choose between different actions according to certain odds, rather than always doing the same thing.

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