In the fourth week, my professor delved further into the complicated aspects of logic and reasoning. By far, this course has been relatively tough for me. I am constantly introduced to new ways of understanding logic, but I struggle to understand the concept that the professor is outlining and the description in the slides. We learnt about concepts ranging from limits and their graphs to outlining proofs and finding them. One thing I struggle to do is find the difference between two seemingly identical expressions. For example, there are two expressions: "xeS1, $yeS2, x + y = 5 & $yeS2, "xeS1, x + y = 5.
with S1 = S2 = {1, 2, 3, 4}. I could not really see the difference between these 2 expressions except for the fact that their conditions switched places.
One thing that I understood was the definition of a graph of x squared as x approaches infinity. In this case, y approaches infinity. My professor explained that y approaches infinity means that y is moving farther and farther away from zero or becoming larger than zero. He also demonstrated the concept of the graph of x squared for x more than zero. Double quantifiers was another concept that my professor explained. He said that they prove that a certain subset of the Cartesian product N X N (N squared) is not empty and has some properties, in 3 ways. I didn't fully understand this concept either as he covered the material quite quickly and I didn't know what to ask him to clarify my doubt. All I knew was that I didn't understand it. This is why I try and review my notes after class to make sense of the content. As well, I aim to further strengthen my knowledge through the help of teaching assistants and also through the detailed course notes.
I also just completed an assignment that combined whatever was taught until last week. It was very challenging, although I did try my best to understand what I wrote and checked my answers thoroughly. Right now, I am quite nervous about the results of this assignment and look forward to the upcoming material in the course.
with S1 = S2 = {1, 2, 3, 4}. I could not really see the difference between these 2 expressions except for the fact that their conditions switched places.
One thing that I understood was the definition of a graph of x squared as x approaches infinity. In this case, y approaches infinity. My professor explained that y approaches infinity means that y is moving farther and farther away from zero or becoming larger than zero. He also demonstrated the concept of the graph of x squared for x more than zero. Double quantifiers was another concept that my professor explained. He said that they prove that a certain subset of the Cartesian product N X N (N squared) is not empty and has some properties, in 3 ways. I didn't fully understand this concept either as he covered the material quite quickly and I didn't know what to ask him to clarify my doubt. All I knew was that I didn't understand it. This is why I try and review my notes after class to make sense of the content. As well, I aim to further strengthen my knowledge through the help of teaching assistants and also through the detailed course notes.
I also just completed an assignment that combined whatever was taught until last week. It was very challenging, although I did try my best to understand what I wrote and checked my answers thoroughly. Right now, I am quite nervous about the results of this assignment and look forward to the upcoming material in the course.
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ReplyDeleteHi Arvind :)
ReplyDeleteWhen I try to make sense of a confusing logical statement, I always try to think of what it means in English by giving all the symbols and predicates some English meaning.
To clarify multiple quantifiers,
I will use another (but similar) example than the one you gave:
1) ∀d∈D,∃b∈B,R(d,b)
2) ∃b∈B,∀d∈D,R(d,b)
D = {set of all dogs}
B = {set of all books}
R(x,y): x can read y
Do you see the difference between 1) and 2)?
1) is saying: For every dog, there is a book that it can read. In other words, every dog can read a book.
2)Is saying: There is a book, such that every dog can read it. In other words, there is a book that every dog can read.
The difference? 1) means that every dog can read some book, but the book that each dog can read may or may not be the same. 2) means that there is this one particular book (the same book) that every dog can read.
@ Double Quantifiers
The slide is just saying that the 3 statements are equivalent.
Hope it helps! If you can any more uncertainties, I am more than happy to help!