Talk:Littlewood conjecture

The article says:

for any two real numbers α and β

$\liminf _{n\to \infty }n\|\alpha -\beta \|,$

where ||x|| is the distance from x to the nearest integer.

I don't understand the difference between this and saying

for any real number α,

$\liminf _{n\to \infty }n\|\alpha \|,$

where ||x|| is the distance from x to the nearest integer.

After all, there are no more real numbers than those that can be written as the difference between two numbers. Michael Hardy 00:39, 15 Aug 2004 (UTC)

The article says that the conjecture is still open as of 2009. However, Peter Sarnak in his memorial notice on Paul Cohen states that the complete solution of the Littlewood Conjecture was achieved (twice, independently) in 1981. There is thus either a conflict of nomenclature (two conjectures, one open in 2009, one solved in 1981) or Sarnak is wrong, or this article is wrong. Gottlob Frege (talk) 19:47, 9 April 2010 (UTC)

Anachronism

Borel is said to have done some work on the conjecture in 1909. Littlewood is said to have proposed the conjecture in about 1930. — Preceding unsigned comment added by 213.123.215.180 (talk) 11:52, 5 October 2015 (UTC)

Borel might have done some work in 1909 that turned out to be relevant to the 1930 conjecture later. — Preceding unsigned comment added by 213.123.215.180 (talk) 11:54, 5 October 2015 (UTC)

The McTutor article on Paul Joseph Cohen speaks of a "significant breakthrough" by Cohen in 1960. — Preceding unsigned comment added by 213.123.215.180 (talk) 12:02, 5 October 2015 (UTC)