It's clear that Snape murdered Dumbledore with the Avada Kedavra curse.
But does that mean Dumbledore is actually dead?
Death is a dicey subject in Harry Potter. Ghosts play integral roles through the stories. Horcruxes can bring Lord Voldemort back to life. Theoretically, if Dumbledore is truly dead, someone could go back in time and change his fate.
If Hermione can use time travel to attend more than her fair share of classes, surely it can be used to bring back to life the greatest wizard of our time.
Even if Dumbledore is dead, it doesn't mean he's out of the picture. And it doesn't mean he's left Harry to fend for himself. Dumbledore could come back as a ghost to offer Harry advice and strategies on how to defeat Lord Voldemort. Dumbledore could come back in Harry's dreams with similar messages of wisdom and encouragement. Dumbledore has a number of means to communicate with the living if he is actually dead.
From that perspective, it doesn't matter if he is alive or dead.
What does matter is that Snape murdered Dumbledore. Snape performed the Avada Kedavra curse, mustered up all the hate and rage he had against Dumbledore, and used it to kill him.
The Avada Kedavra curse will not work unless the user has a true loathing and disdain for its intended target.
Snape would not have used the Avada Kedavra curse unless he truly hated Dumbledore. Harry needed to see that hate and Dumbledore sacrificed himself to strengthen Harry.
Dumbledore's death was a tremendous loss for Harry, the Order of the Phoenix, the students and teachers at Hogwarts. But his death was necessary.
It exposed Snape for what he is: an evil, backstabbing, death eater whose loyalty lies with Lord Voldemort.
More importantly, it freed Dumbledore to complete his task of stopping Lord Voldemort from returning to power.
A dead Dumbledore can influence the living -- Harry in particular -- better than a live Dumbledore.