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Question on a book i am reading.

  1. Jun 27, 2007 #1
    Hi I am reading the book "Introduction to logic and the methodology of deductive sciences" and I'm doing my best on understandig it and so far so good, but I ran to the example of the book: " for any number x, if x=0 or y not equal to 0, then there exists a number z such that x=y.z" I just want somebody to explain the sentential function and what does it mean and please give an example.

    thank you very much.
     
  2. jcsd
  3. Jun 27, 2007 #2
    It means division makes sense.
     
  4. Jun 27, 2007 #3

    HallsofIvy

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    If y is not 0, then z= x/y. If x= 0 then you can take z= 0 whatever y is In either case you have a number z such that x= y.z. Or, as DeadWolfe said, "Division makes sense".
     
  5. Jun 27, 2007 #4
    "Division makes sense" (to quote the other users).

    In a commutative unitary ring R for all non-zero elements that have multiplication inverses. So if a is such an interger then b/a = b*c where c is the multiplicative inverse of b.
     
  6. Jun 27, 2007 #5

    symbolipoint

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    What topic is this, and which named course would contain a study of this topic?
     
  7. Jun 27, 2007 #6
    Sounds like number theory...
     
  8. Jun 27, 2007 #7
    Abstract Algebra.
     
  9. Jun 28, 2007 #8

    In this particular example, the author is trying to make
    points about the scope of the quantifiers (really nothing more).

    Clearly, it's an open formula. So as it stands, it asserts nothing definite. It's neither true nor false. Meaning is really not relevant.
     
    Last edited: Jun 28, 2007
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