Determinacy

In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.

Basic notions

Games

The first sort of game we shall consider is the two-player game of perfect information of length ω, in which the players play natural numbers.

In this sort of game we consider two players, often named I and II, who take turns playing natural numbers, with I going first. They play "forever"; that is, their plays are indexed by the natural numbers. When they're finished, a predetermined condition decides which player won. This condition need not be specified by any definable rule; it may simply be an arbitrary (infinitely long) lookup table saying who has won given a particular sequence of plays.

More formally, consider a subset A of Baire space; recall that the latter consists of all ω-sequences of natural numbers. Then in the game G_A, I plays a natural number a₀, then II plays a₁, then I plays a₂, and so on. Then I wins the game if and only if

Determined (song)

"Determined" is the first single from American band Mudvayne's third studio album, Lost and Found.

Music

The song contains elements of thrash metal and hardcore punk.

Music video

The music video for "Determined" shows the band playing the song in front of a large group of moshing fans. It was recorded in New York City.

Appearances in other media

The song is featured in the soundtrack to Need for Speed: Underground 2.

Live performance

Mudvayne performed the song live for the first time in early 2005 during a small clubs tour. It has since become a regular part of the band's setlist.

Reception

Johnny Loftus of Allmusic called the song "one of Mudvayne's all-time strongest tracks". It also received praise from the Baltimore Sun.

The song was nominated at the 2006 Grammy Awards for Best Metal Performance but lost to Slipknot's "Before I Forget".

Track listing

Sources

External links

Downfall

Downfall may refer to:

Film and television

Literature

Music

List of RahXephon episodes

RahXephon is an anime television series produced by Bones and directed by Yutaka Izubuchi. It was broadcast in Japan on Fuji Television from January 21, 2002 to September 11, 2002. In keeping with the musical theme of the series, episodes are called "movements" and each volume of DVD is called an "orchestration". Each episode has a title screen that provides an English title for that episode, which generally does not correspond to a translation from the Japanese title. In addition to the 26 regular episodes, one recap episode was aired and one episode was released as an (OVA).

The original air dates are schedule dates; these are calendar dates until the April series break, when Fuji Television moved RahXephon from Monday afternoons into a Tuesday late night anime block. Episodes 10 through 26 started at 25:55, which is at 1:55 a.m. Wednesday. This means that the calendar dates of the first and last episode airings are 21 January 2002 and 11 September 2002, respectively. Stations in the Fuji Network System affiliate Tōkai Television Broadcasting network started airing the series in the late night but moved it to late afternoons after the same series break.RahXephon thus remained both a late night and late afternoon anime series throughout its original run.

Downfall (book)

Downfall: The Tommy Sheridan Story is a book by Alan McCombes, former policy co-ordinator of the Scottish Socialist Party (SSP) and editor of the Scottish Socialist Voice, about the political career of Tommy Sheridan, who led the SSP for several years until he was forced to resign amid allegations about his personal life, eventually leaving the party a few years before his eventual conviction for perjury.

McCombes finished writing the book — described by the Scotsman as "the first insider's account of the fall-out from Sheridan's trips to a Manchester swinging club and his ill-fated decision to take on the News of the World after it published details of his sexual proclivities" — less than five months after Sheridan was jailed for committing perjury.

The book was launched on 6 July 2011 at Word Power Books, Scotland's oldest radical and independent bookshop.

Reception

Paul Hutcheon described the book in The Herald as "brilliantly written", adding: "Most tomes on Scottish politics are barely worth reading, but McCombes's offering deserves to be read far beyond Scotland. Although written by a modest man, the book has a savage turn of phrase and a wonderful repertoire of metaphors."