Hi folks, my first post here. I was researching that guy who claims to be the smartest person in the world (Chris Langan) and found thread here… seemed like a good place to ask my question, or submit my observation. So… I'm thinking about 1/9, and I visualize a graph where the ones are slowly converging to zero as they become smaller through the "expanding" regress. And I sat and pondered the argument on wikipedia. 9*1/9 = 1. The convergence proof, right? But I thought, if you're going to assume convergence using the same rules, then why is not the first step, 1/9 = 0, before you multiply it nine times. There isn't a ratio that gives you 0.9…, you have to multiply it to get there, so by order of operations, the steps that get you to .9… should actually get you to zero, if you use the assumption of convergence. How am I wrong?