Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.

Makoto Kawamoto

Makoto Kawamoto (川本真琴, Kawamoto Makoto, born January 19, 1974), is a Japanese pop singer, songwriter and multi-instrumentalist from Fukui, Japan. She currently sings under the pseudonym Tiger Fake Fur.

Biography

Early life

Kawamoto grew up hearing her mother playing the piano. Aside from learning piano, she also studied ballet for about two years and joined the boys' and girls' chorus and took flute lessons. Her life was changed upon seeing a rock festival held in the nearby Prefectural Hall in her high school days. Kawamoto entered the Jin-ai Women's College music department, piano department and formed a band. After graduating from college, Kawamoto found a job at a company and became a piano teacher. However, since she only received a salary of 40,000 yen, she got fed up with her job and quit. Still, she continued to teach piano in her parents' house. She earned her livelihood working at a wedding hall, during which time she continued to try forming a band.

Kawamoto participated in "AIDS against FUKUI" held in Fukui as a band. She wrote the song and made all the members in the hall sing on the pretext of being elected to the executive committee. Because of that, she was invited to Sony’s "Showcase" where amateurs perform live in audition style. Since she was pleased with Tokyo, she saved 1 million yen within half a year, and went to Tokyo at the age of 21. She had a feeling that they liked her performance, but her position was still ambiguous for a while. She worked hard at composition while working part-time in a strange city. Although poor, she lived happily.

Nursery rhyme

A nursery rhyme is a traditional poem or song for young children in Britain and many other countries, but usage only dates from the late 18th /early 19th century. In North America the term Mother Goose Rhymes, introduced in the mid-18th century, is still often used.

History

Lullabies

The oldest children's songs of which we have records are lullabies, intended to help a child sleep. Lullabies can be found in every human culture. The English term lullaby is thought to come from "lu, lu" or "la la" sound made by mothers or nurses to calm children, and "by by" or "bye bye", either another lulling sound, or a term for good night. Until the modern era lullabies were usually only recorded incidentally in written sources. The Roman nurses' lullaby, "Lalla, Lalla, Lalla, aut dormi, aut lacta", is recorded in a scholium on Persius and may be the oldest to survive.

Many medieval English verses associated with the birth of Jesus take the form of a lullaby, including "Lullay, my liking, my dere son, my sweting" and may be versions of contemporary lullabies. However, most of those used today date from the 17th century. For example, a well known lullaby such as "Rock-a-bye, baby on a tree top", cannot be found in records until the late-18th century when it was printed by John Newbery (c. 1765).

Rurouni Kenshin

Rurouni Kenshin: Meiji Swordsman Romantic Story (Japanese: るろうに剣心 -明治剣客浪漫譚-, Hepburn: Rurōni Kenshin Meiji Kenkaku Romantan), also known as Rurouni Kenshin and Samurai X, is a Japanese manga series written and illustrated by Nobuhiro Watsuki. The story begins during the 11th year of the Meiji period in Japan and follows a former assassin from the Bakumatsu, named Known as Hitokiri Battosai. After his work against the bakufu, Hitokiri Battosai disappears to become Himura Kenshin: a wandering samurai who protects the people of Japan with a vow of never to take another life. Watsuki wrote this series upon his desire of making a shōnen manga different from the other ones that were published at the time, with Kenshin being a former assassin and the story taking a more serious tone as it continued. The manga revolves around themes of atonement, peace, and romance.

The manga initially appeared in Shueisha's Weekly Shōnen Jump from April 25, 1994, to November 4, 1999. The complete work consists of 28 tankōbon volumes, while years later it was reprinted into twenty-two kanzenban volumes. Studio Gallop, Studio Deen and SPE Visual Works adapted the manga into an anime series which aired in Japan from January 10, 1996 to September 8, 1998. Besides an animated feature film, two series of original video animations (OVAs) were also produced. The first adapted stories from the manga that were not featured in the anime, while the second was a sequel to the manga. Several art and guidebooks for Rurouni Kenshin have been published and writer Kaoru Shizuka has authored three official light novels which were published by Shueisha. Many video games have also been released for the PlayStation, PlayStation 2, and PlayStation Portable consoles. A successful live-action theatrical film adaptation was released in 2012, with limited international screenings.