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I was reading a note from guardian.uk called What lurks beneath a scientist's lab coat?, a little gallery of geeky-tattoos.

However, number 11 in the series has the following image and caption text:

Nine axioms?

'From these nine axioms,' writes Turing Eret, a software designer in Colarado, 'one can derive all of mathematics – a field you can likely tell that I love dearly'

Is that really so? Are those the nine axioms? (I guess it means the ZF axioms) If so, how are they expressed like that? (Last question meaning: how does that expression imply the nine axioms?)

I tried to search it around but searching formulas is really hard. Also, Google and TinEye image search wouldn't produce anything relevant.

I really suck at math but I love it, so forgive me if I'm asking something stupid.

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No. Those are not the axioms ZF set theory. (To be precise there are infinitely many ZF set theory "axioms". The "nine" axioms actually include a few axiom schema). The picture is that of some statement of lambda-calculus. –  Bill Cook Jan 11 '12 at 1:02
@BillCook Thanks! Took me a while to understand the statement about ZF schematic but re-reading some references, it made sense to me. –  Alpha Jan 11 '12 at 1:12
those were some interesting tatoos. I wonder if any of the other tatoos are as inaccurately labeled as the one you posted above. If so, I'd skip buying the book. :) –  Bill Cook Jan 11 '12 at 1:15
It looks like they just misplaced the caption. Here is an arm (same person?) with ZF (or is it ZFC?) written on it: jux.com/gallery/34661. Google for "carl zimmer" "nine axioms", it is the first link. –  Dan Brumleve Jan 11 '12 at 5:54
Main page of the other gallery of the same work: scienceink.jux.com. Unfortunately it doesn't feature the Y combinator image so who knows what he has to say about it (buy the book?). –  Dan Brumleve Jan 11 '12 at 6:01

2 Answers 2

up vote 6 down vote accepted

It is called a Y combinator. This particular one was invented by Haskell Curry according to the Wikipedia page. It has little to do with set theory and I am not sure what are the "nine axioms" referred to. I know it as being a useful tool in constructing a LISP-like language from combinator calculus. It has the effect of applying its argument to itself, i.e. Yx -> x(Yx) -> x(x(Yx)), which can be used to implement recursion. This is not the only expression with such an effect; scroll down the Wikipedia page to see some other examples of Y combinators.

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That's my arm! Yeah, it was incorrectly labelled in the Guardian article. That is the Y Combinator as others have mentioned. My OTHER tattoo are the ZFC axioms. In the book, both tattoos are pictured but only the ZFC one is described. A bit unfortunate, but oh well. What can you do?

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