Problem: Tamannaah Bhatia was born on 21 December 1989 in Mumbai, Maharashtra, India, to Santhosh and Rajani Bhatia. She has an elder brother, Anand. Her father is a diamond merchant. She is of Sindhi descent.

Tamannaah's first release of 2009 was the Tamil film Padikkadavan, directed by Suraj and co-starring Dhanush, which was named after Rajinikanth's 1985 film of the same name. The film received mixed reviews from critics but Tamannaah's performance in a limited role won praise. Padikkadavan however became a commercial success. Her next release was the Telugu film Konchem Ishtam Konchem Kashtam directed by Kishore Kumar Pardasany and co-starring Siddharth. The film received positive reviews from critics and she received critical acclaim for her performance, earning a nomination at the 57th Filmfare Awards South in the Best Telugu Actress category. The film however was an average grosser at the box office. Her next release, K. V. Anand's Ayan, co-starring Suriya, became the only major commercially successful Tamil film of the year. She later appeared in Gandhi Krishna's Ananda Thandavam which was based on the novel Pirivom Santhippom serialised by Sujatha Rangarajan. She was paired with Siddharth Venugopal in the film marking the latter's debut. The film opened to negative reviews, and was her only commercial failure in 2009. However Tamannaah's performance was critically acclaimed. Pavithra Srinivasan of Rediff.com stated that Tamannaah's "would-be innocence when she's playing up to Sidharth, and slight cunning when she chooses Radhakrishnan is perfect" adding that she brought her character Madhumitha "to life, an alluring mix of child and woman; irritating, sly, yet arousing your sympathy in the climax". Tamannaah later appeared in R. Kannan's Kanden Kadhalai, the official remake of Jab We Met (2007), co-starring Bharath. Her voice was dubbed by playback singer Chinmayi. Kanden Kadhalai opened to decent feedback from critics and Tamannaah's performance won praise from them. A reviewer from Sify stated, "Funny and full of life, it is Tamannaah who is the heart and soul of this love story. She has come up with a live wire performance and the magic of the film lies in her performance", adding that no actress in Tamil cinema could play that role better than her though she did not look like a Thevar girl hailing from Theni. Her performance in the film earned her a nomination at the 57th Filmfare Awards South in the Best Tamil Actress category, making her the only actress to earn two nominations in two different languages at that event. She also won the South Scope award for the same. During this phase, she was established as an undisputed top actress in Tamil cinema. Tamannaah's first release of 2010 was N. Linguswamy's Paiyaa, co-starring Karthi, which was a Tamil road movie. The film opened to positive reviews from critics and was a commercial success. She earned a nomination each at the 58th Filmfare Awards South and 5th Vijay Awards in the Best Tamil Actress category. Her other two releases of 2010 were S. P. Rajkumar's Sura, co-starring Vijay, and M. Raja's Thillalangadi, co-starring Jayam Ravi, the former being Vijay's 50th film as an actor and the latter being the official remake of Surender Reddy's Kick (2009). Both the films flopped at the box office.

what happened in 2009?

Answer with quotes: Tamannaah's first release of 2009 was the Tamil film Padikkadavan,

Problem: Georg Ferdinand Ludwig Philipp Cantor ( KAN-tor; German: ['geoRk 'feRdinant 'lu:tvIc 'fIlIp 'kantoR]; March 3 [O.S. February 19] 1845 - January 6, 1918) was a German mathematician. He invented set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers.

Cantor's 1874 Crelle paper was the first to invoke the notion of a 1-to-1 correspondence, though he did not use that phrase. He then began looking for a 1-to-1 correspondence between the points of the unit square and the points of a unit line segment. In an 1877 letter to Richard Dedekind, Cantor proved a far stronger result: for any positive integer n, there exists a 1-to-1 correspondence between the points on the unit line segment and all of the points in an n-dimensional space. About this discovery Cantor wrote to Dedekind: "Je le vois, mais je ne le crois pas!" ("I see it, but I don't believe it!") The result that he found so astonishing has implications for geometry and the notion of dimension. In 1878, Cantor submitted another paper to Crelle's Journal, in which he defined precisely the concept of a 1-to-1 correspondence and introduced the notion of "power" (a term he took from Jakob Steiner) or "equivalence" of sets: two sets are equivalent (have the same power) if there exists a 1-to-1 correspondence between them. Cantor defined countable sets (or denumerable sets) as sets which can be put into a 1-to-1 correspondence with the natural numbers, and proved that the rational numbers are denumerable. He also proved that n-dimensional Euclidean space Rn has the same power as the real numbers R, as does a countably infinite product of copies of R. While he made free use of countability as a concept, he did not write the word "countable" until 1883. Cantor also discussed his thinking about dimension, stressing that his mapping between the unit interval and the unit square was not a continuous one. This paper displeased Kronecker, and Cantor wanted to withdraw it; however, Dedekind persuaded him not to do so and Weierstrass supported its publication. Nevertheless, Cantor never again submitted anything to Crelle.

What is one-to-one correspondence?

Answer with quotes:
He then began looking for a 1-to-1 correspondence between the points of the unit square and the points of a unit line segment.