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.
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".
"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.
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.