I was brushing up on induction last night. Anyway, there is no base case here. If grandma had given Tommy a present in the past for being a good kid and it had surprised him, Tommy would not have reasoned and concluded that his grandma is a liar. Instead, he would have likely deduced something to the effect “if it happened once, it can happen again”, unless, of course, you get executed during the the base case. Oh look, grandma is giving a present...then all of a sudden ”whack” , your head chopped off. Personally, I like the execution version better.
