Batman: to kill or not to kill
Personally, i don't think Batman should kill the Joker. He was sworn to strike fear into the heart's of Gotham's criminals, killing his long adversary wouldn't make him any better in Gotham's eyes.
As he told the Sewer King in the B:TAS episode "The Underdwellers"..
"I don't pass sentence, that's for the courts. But this - THIS TIME - i am sorely tempted to do the job myself." Batman used those words to instill fear into the Sewer King after the way he treated those children.
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"I've seen things you people wouldn't believe: Attack ships on fire off the shoulder of Orion; I've watched c-beams glitter in the dark near the Tannhauser Gate. All those moments will be lost in time; like tears in rain. Time to die." Roy Batty
Besides, let's face it, it just plain wouldn't work. In the Joker's very first appearance, back in the early days of Detective Comics (I'm thinking in '38, but could be wrong), the Joker did die. And then the writers told us that it wasn't really him, just someone who looked like him - a gag that's recurred over the years. TVTropes.org calls it "Joker Immunity".
Also, since the second rewrite of his origins in the Fifties, Bats doesn't kill. It's a line he's drawn for himself, and what separates him from the criminals more often than not. Sure, he'll break and enter, he'll wiretap, he'll stalk, he'll abduct and unlawfully imprison, sometimes he'll even commit assault - but he won't use guns, and he won't kill. Grayson/Batman is even more committed to the "no killing" thing, since he started off as a circus performer, adopted by Wayne after his parents were killed by the Mafia.
And of course, as the Joker has pointed out a few times over the years, the two of them, as polar opposites, balance each other. The Joker and the Bat are virtually fated to fight for as long as they live, and neither will outlast the other for long. (It's my personal opinion, although not yet explored by the writers since Grayson took over AFAIK, that the Joker has been lying low because he knows it's not his old frenemy under the cowl any more. Without the real Batman, the Joker doesn't think it's worth it. Although if he had the capability, I think the Joker might well go after Darkseid for daring to kill the Bat before the Joker could - and I wouldn't bet against the clown on this one...)
Now, it may well be necessary, in the current storyline, for the Impersonator Joker to die - but I'm also willing to bet it'll be Damien, not Dick, who delivers the killing blow, and then has to endure endless lectures from Dick (and possibly even a small chiding from Alfred) for crossing the line.
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Sodium is a metal that reacts explosively when exposed to water. Chlorine is a gas that'll kill you dead in moments. Together they make my fries taste good.