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Velleman's how to prove it

  1. Jul 18, 2012 #1
    Apparently I've read through Velleman's book halfway a few times and section 2.1 gets me all the time. Its on existential and universal quantifiers. I still don't know how to take a sentence and convert it using predicate symbol quite well. I'm not sure what other sorts of skills i am missing. I need some input on how to better understand predicate logic?
    Last edited: Jul 18, 2012
  2. jcsd
  3. Jul 18, 2012 #2

    Stephen Tashi

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    Is your main goal to learn the predicate calculus? - or are you under the mis-impression that you must learn the predicate calculus in order to understand higher mathematics?

    If your objective is learn higher mathematics such as abstract algebra, advanced calculus, topology and other branches of math that don't focus on "foundations", such as logic and set theory, then my advice is proceed onward to those branches of higher mathematics. It is commendable to study logic as a foundation for understanding math, but your ability to translate sentences into logical expressions with quantifiers will be sharpened by studying higher math because the sentences about mathematical topics will be more precise than common speech.

    As to "other skills", I haven't studied your posts. In my opinion, the most glaring weakness that students have is that they substitute their own private ideas about mathematical objects for the formal definitions. (For example, they have their own notions about whether "dy" and "dx" are numbers, or whether .9999... = 1 or whether [itex] \frac{ \infty}{\infty} = 1 [/itex]) As a consequence, they don't understand how to employ the formal definitions in proofs and they start expressing opinions about symbolic expressions like [itex] \infty [/itex] without considering whether these scribblings have formal mathematical definitions.
  4. Jul 18, 2012 #3
    I'm under the impression that if i don't understand something in this book than i'm missing some other background knowledge. I'm not sure if i should just move on with the rest of the book or stay stuck until I get it.But this is one of the few things that is not clicking in my head.
  5. Jul 18, 2012 #4

    Stephen Tashi

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    You didn't say why you are reading the book. Have you studied calculs yet? If so, do you see how the definitions of the various kinds of limits involve quatifiers and how the proofs involve the logic of quantifiers?
  6. Jul 18, 2012 #5
    The reason why I am reading this book is because I don't have much exposure to writing proofs. I'm reading it over again because I feel that some of it I don't have a good grasp of and quantifiers is one of them. This is the only book I read so far that deals with proofs. I haven't read any other books on proofs.
  7. Jul 18, 2012 #6
    Never mind I found a good book called Schaum's outline of logic. It explains both propositional and predicate logic quite well.
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