Recent content by xouper

Any comments?

Regarding the weak continuum hypothesis (B.F. Jones): {\displaystyle 2^ {\aleph_{0}} < 2^ {\aleph_{1}}} and the Luzin Hypothesis: {\displaystyle 2^ {\aleph_{0}} = 2^ {\aleph_{1}}} Where can I find Bukovsky's paper that shows the Luzin Hypothesis is consistent with set theory? Or perhaps...

In this particular case it doesn't, since several other Schaum's books by Spiegel are also out-of-print and they are dirt cheap. In fact, most out-of-print Schaum's books are dirt cheap.

May I ask, where is there a copy for that price? The book is out of print.

Most used Schaum's Outline books can be gotten pretty cheap, but not this one by Murray Spiegel: http://www.campusi.com/bookFind/asp/bookFindPriceLst.asp?prodId=0070602212 What is it about this particular book that can command such a price?

Perhaps we need to make explicit the distinction between sets and descriptions of sets? A description of a set might be valid under a given set of axioms, but does that necessarily make the set itself valid? In other words, while \{x\,: x\notin x\} might be a valid description in Frege's...

Thanks for all the feedback. You have essentially confirmed what I wanted to know. And thanks also for the set theory review, which I didn't need, but at least confirms we are on the same page, so to speak. :-p Agreed. Not valid in NBG either. Seems to me, however, that is not a valid...

My objective is to show, with a very specific example, that just because a function can be described does not mean it is valid. When Russell described the set of all sets that are not members of themselves, he showed that just because you can describe a set does not mean it is a valid set or...

Sorry. Perhaps I explained my requirements backwards. And perhaps I should have used the Liar's paradox as you noted. My primary requirement is to describe a function that has a domain of N and a range of {0,1}, and to do it with the notation I used in my opening post. This is more...

Good point. In hindsight I see that I was sloppy in my opening sentence. I am not looking to capture the entire Barber Paradox in a function, but rather only the essence of the question, "Does the barber shave himself?". Also, I used \mathbb{N} as the domain for reasons not related to the...

Agreed. I suspected as much but it is nice to see someone else say it explicitly. Using the definition of a function at mathworld, I infer that my "function" is not a function because it does not seem to uniquely assign a value to f(n). But that's exactly what I want, something that looks...

Regarding the Barber of Seville paradox, I am looking for something equivalent that is expressed in functional notation. For example, this is my attempt at a piecewise definition of such a function: For a function f : \mathbb{N} \mapsto \{0,1\} f(n)=\left\{\begin{array}{cc}0,&\mbox{ if...

For a function f : \mathbb{N} \mapsto \{0,1\}f(n)=\left\{\begin{array}{cc}0,&\mbox{ if }f(n)=1\\1,&\mbox{ if } f(n)=0\end{array}\right.