Recent content by xwolfhunter

I'm reading Gelfand's algebra, and I encountered some wonky stuff that I can't figure out on my own (hence my need for the book in the first place) in problem 42 of the book. Here is an explicit statement of the problem. I thought parts a. and b. were easy, but when it came to part c., I just...

Ahhhh, okay. So by "primitive" he means "irreducible", and that's what should have tipped me off. Right? Thanks, now I can move on. Man, I totally should have seen that. Disappointing.

In discussing proportions (a topic to which I have not been properly exposed) Legendre states that, adding the antecedent of a proportion to the consequent, and comparing the sum to the antecedent, one obtains a proportion equal to the original plus unity. Legendre's book is apparently...

I definitely appreciate that, I have a new context in which to view the book as I go along. If the book becomes boring, I won't think twice before I switch it up. Thanks.

Then I'll simply use it to clear the cobwebs from my mind. I would imagine that if mathematicians can do math in multiple fields of mathematics, it will not be so much of a stretch to assume that I can do the same, and if the text is really so absolutely useless, then in three years there will...

So . . . you're saying that, if I read the whole of the Principia Mathematica, my mathematical visualization and clarity, my understanding of how the rules of logic are to be used, my familiarity with proofs, my working memory, etc., will be entirely unaffected? I would not argue (I would not...

Sad that a work to which a man devoted many years of his life will ultimately be forgotten, I mean. I can learn a whole heck of a lot from my rough draft copy of the Principia Mathematica, about logic and about thinking in general, and since that's what I have, I might as well do that. Thanks...

I had posted a question in the mathematics forum about some conceptual issues I was encountering while reading the book, but now I realize as I read on that I may need a dedicated thread for asking questions about the book. So I am asking two things in this thread. Firstly, I am asking someone...

And now I see the difference between a logician and a mathematician! So I'm at a crossroads, I see. Or, as is the case with me, as a whetstone for my mind. Also, I read that a recurring nightmare of Russell's was that the last copy of his Principia was, in the far future, tossed in the...

Well it's not so much a contradiction . . . he explicitly says that ##\phi x## is a propositional function, and then explicitly says that the propositional function corresponding to ##\phi x## is ##\phi \hat{x}##, and thereafter he says that anything of the form ##\phi \hat{x}## is a...

I know that this book is both fundamentally flawed and an extremely important book. I got it for Christmas, and I kind of view it like a whetstone for my mind. I'm taking my time and I won't turn the page unless I understand everything beforehand. I've been on the same page for a little bit...

Okay . . . I've got this. The last term in what I wrote represents the cardinality of the intersection of all of the sets. I wanted to have something that iterates through all possible combinations of two sets intersecting, and subtracts the cardinality of each one individually. The concept...

Firstly, as I said in my first post, I am not asking about the math, I'm asking about the notation. Secondly, the ##n-1## means "iterated (the number of sets minus one) times." There are no numbers to add, intersect, or unite. The iteration description is exactly the same as that of sigma...

Yeah, I don't get it either. I think your notation just kinda floats there like a lump of seaweed. By "iterator" I meant "algorithm," I suppose. I was basically asking if there is some operator that says "hey, just iterate whatever's in the parenthesis ##n## times and do ##x=x+1## each time."...

I'm currently reading a textbook for one of my classes (discrete mathematics), and we're doing set theory right now. This is not a question about how to do mathematics, it's about how to properly express through notation the concept I'm trying to convey. The text invites the reader to come up...