@robjohn I know what you're thinking, 'cause right now I'm thinking the same thing. Actually, I've been thinking it ever since I got here: Why oh why didn't I take the BLUE pill?
In mathematics, the axiom of regularity (also known as the axiom of foundation) is one of the axioms of Zermelo-Fraenkel set theory and was introduced by . In first-order logic the axiom reads:
:\forall A (\exists B (B \in A) \Rightarrow \exists B (B \in A \land \lnot \exist C (C \in A \land C \in B))).
Or in prose:
:Every non-empty set A contains an element B which is disjoint from A.
Two results which follow from the axiom are that "no set is an element of itself," and that "there is no infinite sequence (an) such that ai+1 is an element of ai for all i."
With the axiom of dependent...
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo-Fraenkel set theory.
Formal statement
In the formal language of the Zermelo-Fraenkel axioms, the axiom reads:
:\forall A \, \forall B \, ( \forall C \, (C \in A \iff C \in B) \Rightarrow A = B)
or in words:
:Given any set A and any set B, if for every set C, C is a member of A if and only if C is a member of B, then A is equal to B.
(It is not really essential that C here be a set — but in ZF, ev...
In short (and from my personal viewpoint), the deepest reason is that the perception is that we will able to build a very functional and enthusiastic community if it's an Mma-only site. E.g. I don't think we could have attracted so many respected experts to commit if it's a general site. The there are the other simpler reasons discussed on the page I linked to
This of course sounds very subjective and it's difficult to show to someone who's not already in the StackOverflow mathematica community, but personally I think that among all other possible and discussed reasons, this is the drive behind the choice
@JM Do you happen to know if you have a certain drug (by that Belgian pharma company) first in oral pill form and then in oral solution if the effect can differ even if you take the same dose (the uptake might be different, for example)?
@robjohn Catholic priests go to every house here and "bless" (I don't know the proper English word) them. They write "GMB + 2012" on the door. I don't know the exact details because my family is protestant.
@JM I mean I saw that someone had this gravatar already. I might have been you, I am not exactly sure
@robjohn I like to play with graphics in Mathematica. Do you still have your Christmas gravatar somewhere? I like that there are so many "fun" features (even in early versions there was easy declarative graphics, sound generation, animation, and now we have MIDI)
@Szabolcs That's one thing I liked about it. Back in the day, I was heavily using POV-Ray. It didn't take much for me to adapt to Mathematica's graphics.
Now that I think about it, I could have done a monochrome snowflake for Christmas...
After seeing this, I wonder about the series $\sum\limits_{n=1}^\infty \frac{q^{n^2}}{n^z}$. It's like the unholy marriage of a Dirichlet and theta series...
@AsafKaragila It's PHD thesis. But not having the source code, perhaps the most useful information from there is: The actual LATEX style is my own modification of the tufte-latex package developed at [Kle].
@AsafKaragila I'm not sure about that. Maybe both?
@Srivatsan Oh, well... I did not have too much of a chance while I was driving my son around, and then I got into writing up an answer I had been working on.
All of them, really. They're not exceptional among questions here (maybe in that they're well written) but for me it's that one of the best number theorists in the world is poking around and asking about simple things.