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December 1

Ackermann vs. tetration

What's the simplification for, or closest common order to, O(A(n,n) / ⁿn)? For O(A(log* n, log* n) / ⁿn)? Neon Merlin 05:58, 1 December 2008 (UTC)[reply]

Unbounded utility

Is there any tangible good for which an unbounded utility function would be realistic? Neon Merlin 06:28, 1 December 2008 (UTC)[reply]

This depends entirely on your understanding of Utility. If you're using ordinal utility (that is to say, utility only represents relative preference, i.e. only the level sets of the function matter), then any bounded function can be transformed into an unbounded one, and vice versa, via use of appropriately scaled tangent and arctangent functions. RayAYang (talk) 06:47, 1 December 2008 (UTC)[reply]

Pascal's Wager is like that, but as I think the goods are hardly tangible and a load of rubbish I'm not advocating it. Dmcq (talk) 12:18, 1 December 2008 (UTC)[reply]

Root at top of tree?

Why is the vertex at the top of a tree called the root? Why not name it after something that would be found at the top of a tree, like a star or an angel? Neon Merlin 07:27, 1 December 2008 (UTC)[reply]

Well, whether trees grow right-side-up or upside-down is convention. Presumably whoever named it root had them grow right-side-up. Mine grow upside-down, but that's just what I'm used to; I'm not going to argue that it's a better or worse convention. It's just the one descriptive set theorists traditionally use. (When I taught descriptive set theory I told the class, just offhand, that they were "Australian trees".) --Trovatore (talk) 08:14, 1 December 2008 (UTC)[reply]

I've seen it done both ways, and I imagine everybody has. Michael Hardy (talk) 12:10, 1 December 2008 (UTC)[reply]

And also because the word "root" implies an origin or something fundamental - for example, "the root of the problem", or "root access on the server". So the name itself is fairly logical, it's more the placement (which I suspect may have something to do with the way the human brain likes to process information). Confusing Manifestation(Say hi!) 05:45, 2 December 2008 (UTC)[reply]

Because the other ends are called the leaves, which makes sense no matter which way you orient your diagrams. Tesseran (talk) 06:18, 2 December 2008 (UTC)[reply]

Wireframe cube result

Having solved a given problem I was surprised to be able to find no reference to its type. Different digits were to be allocated to the edges of a cube so that the sum at each vertex was the same and the sum round each face was the same. It was easy to show that the sum of all 12 digits had to be a multiple of 12, the vertex sum being one quarter of this and the face sum one third. Further, the six pairs of diagonally-parallel edges (top front and bottom rear, for example) had the same sum of one sixth that of all the digits. A solution using the digits 1 to 15, omitting 2, 8 and 14, was straightforward. Is this "wireframe magic cube" generally familiar?→81.153.219.45 (talk) 19:44, 1 December 2008 (UTC)[reply]

I haven't heard of it, but I'm wondering about your use of the word "digit". You appear to consider the number 15 to be a "digit". Did you mean simply positive integers? Michael Hardy (talk) 00:43, 4 December 2008 (UTC)[reply]

Yes - digit was the word in the problem as given, which was simply used without proper thought.→86.132.167.79 (talk) 12:50, 4 December 2008 (UTC)[reply]