Question: The Bee Gees were a pop music group formed in 1958. Their lineup consisted of brothers Barry, Robin, and Maurice Gibb. The trio were successful for most of their decades of recording music, but they had two distinct periods of exceptional success: as a popular music act in the late 1960s and early 1970s, and as prominent performers of the disco music era in the mid-to-late 1970s. The group sang recognisable three-part tight harmonies; Robin's clear vibrato lead vocals were a hallmark of their earlier hits, while Barry's R&B falsetto became their signature sound during the mid-to-late 1970s and 1980s.

At Eric Clapton's suggestion, the brothers moved to Miami, Florida, early in 1975 to record. After starting off with ballads, they eventually heeded the urging of Mardin and Stigwood, and crafted more dance-oriented disco songs, including their second US No. 1, "Jive Talkin'", along with US No. 7 "Nights on Broadway". The band liked the resulting new sound. This time the public agreed by sending the LP Main Course up the charts. This album included the first Bee Gees songs wherein Barry used falsetto, something that would later become a trademark of the band. This was also the first Bee Gees album to have two US top-10 singles since 1968's Idea. Main Course also became their first charting R&B album.  On the Bee Gees' appearance on The Midnight Special in 1975, to promote Main Course, they sang "To Love Somebody" with Helen Reddy. Around the same time, the Bee Gees recorded three Beatles covers--"Golden Slumbers/Carry That Weight", "She Came in Through the Bathroom Window" with Barry providing lead vocals, and "Sun King" with Maurice providing lead vocals, for the unsuccessful musical/documentary All This and World War II.  The next album, Children of the World released in September 1976, was drenched in Barry's new-found falsetto and Weaver's synthesizer disco licks. Mardin was unavailable to produce, so the Bee Gees enlisted Albhy Galuten and Karl Richardson, who had worked with Mardin during the Main Course sessions. This production team would carry the Bee Gees through the rest of the 1970s.  The first single from the album was "You Should Be Dancing" (which features percussion work by musician Stephen Stills). The song pushed the Bee Gees to a level of stardom they had not previously achieved in the US, though their new R&B/disco sound was not as popular with some die hard fans. The pop ballad "Love So Right" reached No. 3 in the US, and "Boogie Child" reached US No. 12 in January 1977. The album peaked at No. 8 in the US.  A compilation Bee Gees Gold was released in November, containing the group's hits from 1967 to 1972.

Using a quote from the above article, answer the following question: what do you find interesting in the article?
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Answer: Barry used falsetto, something that would later become a trademark of the band.

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.