Talk:Littlewood conjecture

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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)