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It was just a stroke of bad luck. There is absolutely <em class='bbc'>no</em> reason anyone, including you, should think you're useless as a person just because you broke an arm. A friend of yours will most definitely not be disappointed, I assure thee.
Try to stay positive. I know that's difficult sometimes(from personal experience), but I'm sure you can do it. Soon your arm will heal, and no one will have hated you for it...or at least, they <em class='bbc'>shouldn't.</em>
I hope your left arm heals quickly. And remember: you haven't fallen until you <em class='bbc'>tell yourself</em> you're down.