I'm a bit confused about lexicographic preferences and whether they abide by the strict monotonicity axiom.
The definition we were given for strict monotonicity is:
For any two bundles $x$ and $y$, if $x_i \succsim y_i$ for each good $i$, then $x$ is strictly preferred to $y$
The preferences are summarized below:
(1) The bundle that has more of good 1 is better, regardless of the amount of good 2.
(2) If the amount of good 1 is the same, the bundle that has more of good 2 is better.
I'm confused about part (1), because a bundle can have much more of good 2 but still be preferred if it has a bit more of good 1, e.g. $(2,5)$ is preferred to $(1,100)$, even though it has so much more in it. Surely that can't follow the provided definition of strict monotonicity (or am I really thick)?