A dice is thrown repeatedly until as six comes up. What is the sample space of the experiment?

It may be that on the first throw, a six comes up or on the first throw, the six does not come up. Thus a six may come up on first throw, second throw, third throw ……. or at the end of infinite number of throws. Thus the sample space would be as:

S = {6, (1, 6), (2, 6), (3, 6), (4, 6), (5, 6),
{(1, 1, 6), (1, 2, 6), …….. (1, 5, 6)},
{(2, 1, 6), (2, 2, 6) …….(2, 5, 6)} …….}