Two angels are playing a game, the rules of the game are as follows: on turn 1 angel 1 names a number greater than 0 and less than 1, then the angels alternate turns, picking a number greater than the last number named by the other angel, if they can't name a larger number less than 1, that angel loses the game

After infinite turns, does an angel win the game? and if so, with what number? is it possible for an angel to win on the first turn?