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