Prod

Prod or PROD may refer to:

Product integral, often shown using the symbol

Empty product

In mathematics, an empty product, or nullary product, is the result of multiplying no factors. It is by convention equal to the multiplicative identity 1 (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no numbers—is by convention zero, or the additive identity.

The term "empty product" is most often used in the above sense when discussing arithmetic operations. However, the term is sometimes employed when discussing set-theoretic intersections, categorical products, and products in computer programming; these are discussed below.

Nullary arithmetic product

Justification

Let a₁, a₂, a₃,... be a sequence of numbers, and let

be the product of the first m elements of the sequence. Then

for all m = 1,2,... provided that we use the following conventions: and . In other words, a "product" with only one factor evaluates to that factor, while a "product" with no factors at all evaluates to 1. Allowing a "product" with only one or zero factors reduces the number of cases to be considered in many mathematical formulas. Such "products" are natural starting points in induction proofs, as well as in algorithms. For these reasons, the "empty product is one convention" is common practice in mathematics and computer programming.

Mudvayne

Mudvayne is an American heavy metal band from Peoria, Illinois formed in 1996. Originally from Bloomington, Illinois, they are known for their sonic experimentation, innovative album art, face and body paint, masks and uniforms. The band has sold over six million records worldwide, including nearly three million in the United States.

The group consists of Chad Gray (lead vocals), Greg Tribbett (guitar, vocals), Ryan Martinie (bass guitar) and Matthew McDonough (drums). Formed in 1996, Mudvayne became popular in the late-1990s Decatur, Illinois underground music scene. The band released an EP, Kill, I Oughtta, in 1997 and a successful debut album, L.D. 50, in 2000. They had global success with The End of All Things to Come, Lost and Found and The New Game.

Since 2010, the band has been inactive, with its members performing in other projects and making guest appearances. Chad Gray is the vocalist for the heavy metal supergroup Hellyeah, to which Greg Tribbett also belonged until 2014. Gray founded an independent record label, Bullygoat Records, which produces heavy-metal albums. In early 2015, Chad Gray noted that the band's return at the moment seems very unlikely, unless "everybody licked their wounds and got over it".

Mudvayne (album)

Mudvayne is the fifth studio album by the American metal band Mudvayne and their most recent to date. It was released on December 21, 2009. The material from the album was recorded simultaneously with the material that appeared on The New Game. "Beautiful And Strange", a single from the band, was made available for streaming on the band's website and MySpace page on October 7, 2009. There was no tour to support the album, which had little promotion; sales were also weak.

Production

Following the release of Lost and Found in 2005, Chad Gray and Greg Tribbett formed the heavy metal supergroup Hellyeah. They released their self-titled album in 2007. The following year Mudvayne released their fourth album The New Game to lukewarm reviews. Chad Gray has said "I love being in two bands. I really do. You get to explore both sides of yourself. I think everybody has this severed half. The kind [that] co-exists outside of your work. I was able to kind of climb into that skin."

The album was produced by Jeremy Parker and David Fortman.