What does "inf{ . }" stand for in probability theory?

Question

The full statement was G(u)^-1 = inf{y | G(y) >= u }

Where,
G(y) is a cumulative distribution function,
G(u)^-1 is its inverse
and u seems to be a point in the unit cube.

Answer 1

That means the greatest lower bound or infimum
http://mathworld.wolfram.com/Infimum.html
http://www.ee.ic.ac.uk/hp/staff/dmb/prob/distrib.html

Answer 2

There is a thing called 'infimum', abreviated inf, of a set.

The inf of a set is the largest lower bound. It comes from the limiting behavior of infinite sets, which is why it's not just the smallest element of a set.

That equation appears to be saying that

1/G(u) equals the smallest y such that G(y)=>u

Sounds interesting. What's the context? I'm a stat specialist and would like to look it up.

Why would you say that u is a point in the unit cube since G(y) is a one dimensional density.