So it boils down to what is being represented: an amount of items versus an amount of _boundaries_ across items.
When I'm booking that stay between Jan 13th and Jan 14th, and I am presented with options, the ones that say "sleeps 2" does not mean [1, 2) but rather [1, 2] and the one that says "sleeps 6" does not mean [1, 6) but rather [1, 6].
When looking for a booking you are using an interval.
When looking at room capacity you are looking for a minimum. This is not the same as an interval. If you are looking for "sleeps 6" that is your bare minimum acceptance in capacity. You are not interested for the [1, 6] interval. Nothing below 6 makes sense.
Even if you wanted to force the interval use here, I'd say you'd be looking for the [6, INF) interval. That is, rooms with capacity of at least 6 (but having more capacity is fine).
When I'm booking that stay between Jan 13th and Jan 14th, and I am presented with options, the ones that say "sleeps 2" does not mean [1, 2) but rather [1, 2] and the one that says "sleeps 6" does not mean [1, 6) but rather [1, 6].