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Just a layman and slow learner. Thank you for your enlightenment and patience, and for giving me the best memory in my life.


Aug
14
comment Is a set of some $m \times n$ matrices a relation?
I am now ignoring the operations on the matrices and therefore any algebraic structure on the set of some matrices, just think a n by m matrix as a n by m array please. @whacka
Aug
14
comment Is a set of some $m \times n$ matrices a relation?
@whacka: See the first line i just updated in my post. So what is a set of matrices, something more sophisiticated than a nm-ary relation on $\mathbb R$? Thinking it as a nm-ary relation on $\mathbb R$, will lose the dimension and size of the matrices.
Aug
14
comment Is a set of some $m \times n$ matrices a relation?
@whacka: The question in my post is: Is a set of some n×m real matrices a relation or something more sophisicated? I haven't put any operation on the set of matrices yet, and the set can consist of any matrices or not.
Aug
14
comment Is a set of some $m \times n$ matrices a relation?
@whacka: $A$ and $B$ are two arbitrary sets. see the definition of a relation.
Aug
14
comment Is a set of some $m \times n$ matrices a relation?
@ShawnO'Hare: The question in my post is: Is a set of some n×m real matric a relation or something more sophisicated?
Aug
14
comment Is a set of some $m \times n$ matrices a relation?
No, because from $\mathbb R^{nm}$, you can't tell it is two dimensional. A vector and a matrix are never the same.
Jul
25
comment Is this theorem about soundness or completeness?
Thanks. How do you like Kaye's book? What level would you classify it into, with what similar books?
Jul
24
comment statements, propositions, formulas, and wffs
Thanks. In propositional logic, is every wff a sentence? Is every wff also called a proposition, although there is no semantics yet?
Jul
23
comment Is there no propositional letter in first order logic?
why are they left out?
Jul
23
comment Is there no propositional letter in first order logic?
Are True and False atomic formulas? The book doesn't say so, but I think so.
Jul
23
comment Is there no propositional letter in first order logic?
thanks. Why are there propositional symbols in propositional logic?
Jul
23
comment statements, propositions, formulas, and wffs
Thanks. In propositional logic, is every wff a sentence? Is every wff also called a proposition, although there is no semantics yet?
Jul
23
comment separating propositons with commas?
@copper.hat what does "mistake trail" mean?
Jul
23
comment separating propositons with commas?
@Git: (1) WHat does "a set of formulas on the LHS of the turnstile symbol" mean? "AND" of the formulas, or "OR" of the formulas, or ...? (2) Does a comma between formulas mean "AND" of the formulas?
Jul
23
comment separating propositons with commas?
@copper.hat, I see one formula, not a set of formulas on the LHS?
Jul
23
comment separating propositons with commas?
@Git: (1) why is the LHS a set? I think it is a boolean term, not a set. (2)since we have $∧$, why do we need comma?
Jul
23
comment separating propositons with commas?
(1) First of all, by $\{a∧b\}$ do you mean it is a set? why is the LHS a set? Isn't it a boolean term? (2) WHere is "comma"?
Jul
23
comment What does “calculus” mean?
be back later. @GuyCoder
Jul
21
comment Are variables logical or non-logical symbols in a logic system?
The link says "The non-logical symbols of a language of first-order logic consist of predicates and individual constants. These include symbols that, in an interpretation, may stand for individual constants, variables, functions, or predicates. A language of first-order logic is a formal language over the alphabet consisting of its non-logical symbols and its logical symbols. The latter include logical connectives, quantifiers, and variables that stand for statements."
Jul
21
comment Are variables logical or non-logical symbols in a logic system?
thanks. (1) I mixed up variables for the arguments to quantifies, and variables representing propositions. (2) the former is non-logical, while the latter is logical symbols, according to en.wikipedia.org/wiki/Non-logical_symbols