SLOG #1

    This week has been both exciting and confusing for me. I very much enjoyed learning and absorbing new information in class, but was occasionally perplexed by the unusual concepts. I say "unusual" because the concepts differ from everyday common sense. Specifically, I had difficulty grasping two ideas discussed in lectures.
    The first idea is verifying universal claims.  The notes explain "to verify a universal claim, show there is no counter-example". The explaination looks great at first glance. If I want to verify all the coins in my wallet are quarters, I should look through them and find no penny, nickel, dime, loonie, or toonie. Simple enough. However, I could not accept the idea that empty sets consist of no element, therefore no counter-example, resulting in a situation that all universal claims are true. If I applied that to the coins-in-my-pocket example, it would be equivalent of claiming, with correctness, "all the coins in my pocket are quarters", despite my pocket being empty. In order to wrap my head around this I had to carefully look over the lecture notes once again, and understand that "to verify a universal claim, show there is no counter-example" is not just stating the obvious. It is defining a method of verification.
    The second idea is implication. In particular, the lack of causality in "if... then..." statements and the "vacuous truth" aspect. I must admit that I was completely baffled when I read the notes "If you eat your vegetables, then you can have dessert.... in logic, we allow the case where you don't eat your vegetables and still eat dessert to be consistent with the implication." I kept wondering, for that specific example, how one can be allowed to have dessert without eating vegetables. Only after reading some course notes pertaining to "vacuous truth" did I begin to accept the above concept, that regardless of the consequent, so long as the antecedent is false, the implication will ring true due to the empty (true antecedent) set's property of belonging to any set (true set for consequent).