Recent content by samp

Suppose we have a statement A that holds if and only if statement B holds. "A if and only if B" I'm fairly sure I read before that this does not necessarily mean that A and B are identical: in general, A <--> B does not imply A = B. I'm having difficulty determining how A and B could be...

Thanks, everyone, for your replies. However, I'm still having trouble. This is really hard for me, and I feel dumb for failing to perceive something so simple. Here's my next question that may put the issue to rest, for me. What would be a good definition for empty set, that relies in no...

What exactly is a set with no elements? What does it mean? Aren't sets entirely defined by their contents? In what manner is a set with no contents defined? I'm not arguing for or against such an axiom... I simply want to know what the axiom actually is saying. If an empty set is not...

thanks :)

When ending a sentence with ellipses, do I also include a period (3 or 4 dots)? \cdots or \cdots . ?

Well, don't keep me waiting! What's the answer? :confused: :smile:

I once had such thoughts, but as it turns out I was just high on DXM. *moves to close this thread*

Umm... What?!

What is an aspect of consciousness that is not purely subjective?

Does anyone know of a blog or plug-in for a blog that can do this? Linking a pdf/ps/dvi attachment for each post in my blog that I make that has even the slightest bit of math in it seems silly. At the same time, I want the math to be legible.

That's why we choose universes smaller than "everything". Thinking about the set of all sets just leads to a headache.

I'm not sure where this should go - I didn't see any LaTeX-related forum. Is there a way to create a horizontal rule that doesn't take up the entire width of the page? Thanks, Sam