It is nearly impossible to die by slitting your wrists.
Although there is an artery in that area, it's small and usually will clot off before it does much damage.
Besides, dying by bleeding to death is VERY painful. I know, as I almost died from a bleeding ucler in 2006, I lost over 50% of my body's blood volume. The pain is not unlike being hit by an 18 wheeler, and it takes a very long time to die.
First you get so weak that you can't even walk, then your muscles start to cramp up, then towards the end everything starts to scream for oxygen and blood, and you know you're going to die because you've never hurt so bad, or felt so horrible.
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