There is always the old conundrum of whether logic "came before" mathematics of vice versa. I know I express my prejudice in asserting the first and surely agree with the micromass that one has to be knowledgeable w/ ZFC axioms before attacking math.
As to the "best" work on set theory...
Thank you for your reply HallsofIvy. This is precisely the point I see. Rosser (Logic for Mathematicians – 1953 – p. 279) states: “Actually, Peano stated his axioms for the positive integers, rather than for the negative integers. However, his axioms are just what the above five statements...
Peano's Postulates 1889 – In Original Italian
Nel 1889 pubblica Arithmetices Principia nova methodo exposita opera, tutta in latino, famosa in tutto il mondo: la teoria dei numeri naturali si sviluppa a partire da cinque semplici proprietà (gli assiomi di Peano):
I. Uno è un numero...
Elementary set theory has been taught to grammar school kids; they called this the "new math" back in the '60s. Now, if you want a formal and more complex treatment of it, where proofs are involved, it doesn't hurt to have a symbolic logic course. Barring that, as g_edgar states, any course...
In 1997 I did considerable research on the reasoning behind the precedence of logical operators in a parenthesis-free notation, asking why certain ones took priority. Obviously, there has to be an agreement for the convention; otherwise, there would be no consistent computations. Yet, I really...
Re: "Absence of evidence is not evidence of absence", I see both words being used as things and properties of individuals. "Absence" in the first part is a quality that the thing "evidence" has. In the second, "absence" is the thing that possesses the quality of being evidence. Thus, to...
For anything having to do with questions such as "Find minimum/max. possible of ONLY A such that B is minimum/maximum - how to do these type of questions? " and Venns, if I recall correctly, fuzzy set theory should cover this. Also, for advanced topics, more than three circles can be used for...
The confusion here, I think, is in the designator "X", where this letters is trying to stand for both an element as well as a set. {X} in X means the element X as a set is found within the set, which violates the axiom of regularity, otherwise called "axiom of foundation", designed to prevent...
These, and there are numerous interactive ones, both with Venns and using the standard form method. I learned all this stuff PRE-internet, but this spring I was tutoring someone in logic, and it is amazing how many resources are available; we never had it this good! Kids today are spoiled...
tauon is right about the typo. Adding a step or so will reveal why:
Original -
(¬P V R) V (¬Q V R)
= (¬P ∧ ¬Q) V R
New -
(¬P V R) V (¬Q V R)
(¬P V (R V ¬Q) V R) Association
(¬P V (~Q V R) V R) Commutation
(¬P V ~Q) V (R V R) Association
(¬P V ~Q) V (R) Idempotence
The conjunct...
Several items:
There is a 16 column Table of Functional Completeness that contains not only Boole's four traditional operators, functions, or connectives - however you want to term them, but 12 others, such exclusive or, nor, nand, tautology, reverse implication, and contradiction. Each of...
As to the comment by SW VandeCarr, I see that we may have a type theory problem, here. On one hand, we have an algorithm that generates a sequence, such as found in pi, and then the result, the exactness which we cannot predict. One might liken in a loose way the algorithm - division - to a...
For standardizing a syllogism - putting it into standard form - simply type in "standard form for syllogisms" and boodles of tutorials will pop up. It is best to know this method, as well as that for Venn diagrams; both can cross check each other, and most logic professors will require you to...
Somewhat of an elaboration on honestrosewater:
A formalization of set theory refers to variables as object language entities. That is, the formalization is a metalanguage talking about things - object language -like symbols (including those for variables and constants) and expressions. This...
Just caught this:
Quantum123 asks in this forum Old Dec25-10, 04:37 PM , "What is an initial segment? " and then says Unread T, 06:16 AM referring to to my post and Suppes, "The book did not even define initial segment properly." If quantum123 does not know what an "initial segment" is, how...