I disagree with the assumption that deciding to live necessarily implies the belief that life has meaning/value. The nihilist is free to choose anything for any reason, or for no reason at all. It’s all meaningless, but that doesn’t prohibit one from making a meaningless decision. I can decide to kill myself/continue living because it’s a Wednesday. It really doesn’t matter why, because there doesn’t even need to be a “why.” Nihilists don’t have to be logical or rational, or make decisions based on emotion or passions.