Suppose it's your birthday, and you get your Aunt (who has an infinite amount of money in the bank) to mail you a signed check with the dollar amount left blank. Your Aunt says you cash the check for any amount you want, provided it is finite. Assume that the check will always go through, and that each extra dollar you request gives you at least some marginal utility. It seems in this case, every possible course of action is irrational. You could enter a million dollars in the dollar amount, but wouldn't it be better to request a billion dollars? For any amount you enter in the check, it would be irrational not to ask for more. But surely you should enter some amount onto the check, as even cashing a check for $1 is better than letting it sit on your dresser. But any amount you put onto the check would be irrational, so it seems that you have no rational options. Does this mean that the concept of "infinite value" is self-contradictory? If so we have a rebuttal to Pascal's Wager.