but the problem can also be resolved mathematically without assuming a maximum amount. nalebuff (1989), christensen and utts (1992), falk and konold (1992), blachman, christensen and utts (1996), nickerson and falk (2006), pointed out that if the amounts of money in the two envelopes have any proper probability distribution representing the player's prior beliefs about the amounts of money in the two envelopes, then it is impossible that whatever the amount "a=a" in the first envelope might be, it would be equally likely, according to these prior beliefs, that the second contains "a"/2 or 2"a". thus step 6 of the argument, which leads to "always switching", is a non-sequitur, also when there is no maximum to the amounts in the envelopes.