Saturday
October.4th Sunny
Hello everyone!
At first, let me talk about something new
we learned in class. This week, we learned how to transform implications into
conjunctions. Although these are very basic rules in our proof, they are really
helpful for us to identify and understand the negation of each statement.
However, even though transitivity is allowed in implications and conjunctions,
they are still two absolutely different symbolizations. The difference is especially
obvious when we are choosing existential or universal claims, which is the
second important part we learned this week. We can switch two universals in a
claim or two existentials in a claim. This kind of switching does not change
their meaning. However, We are not allowed to switch existential and universal
in a claim, since they would stands for another idea(Think about the example we
talked about in class: “∀x∈S1, ∃y∈S2, x + y=5” and “∃y∈S2, ∀x∈S1, x + y=5”),
even if there is one existential in two universals.
The third lecture of this week is the one that
I enjoyed mst this week. Professor Danny just simply introduces infinity and
proofs because assignment 1 was due this week on Friday and we spent a lecture
in asking questions about assignment 1. As I just mentioned in the first
paragraph, implication is not the same thing as conjunction. This is also the
most important idea which our instructor wants us to understand. I believe that
we will use this idea in many of the remaining part of our course.
Tutorial Exercise and questions in notes
help me go over materials covered this week, so I feel confident about these topics.
I think my achievement is to be familiar with not just things we learned this
week, but also everything we was taught during the past several weeks. At the
end, I hope everyone would get a good mark in next week test.
See you next week :)
Cecilia
