[Note, after rereading your post my comment is tangential]
I have always been empathetic to the argument, from people first presented with this, that they are different. Understanding how math deals with infinity basically requires having the mathematical structure supporting it already known. I’m not particularly gifted at math, but the first 4 weeks of real analysis really changed the way I think, because it was basically a condensed rapid upload of centuries of collaborative work from some of the smartest men to ever exist right into my brain.
Otherwise, at least in my experience, we operate in a discrete world that moves through time. So, what I predict is happening, is that when you ask that question to people their best approximation is a discrete world ticking through time.
Is 0.999...=1? Well, each tick of time another set of [0.0...9]’s is added, when the question is finally answered the time stops. You’re then left with some finite number [0.0..01]. In their mind it’s a discrete algo running through time.
The reality that it’s a limit that operates absent of time, instantaneously, is hard to grasp, because it took brilliant men centuries to figure out this profoundly unintuitive result. We understand it because we learned it.
[Note, after rereading your post my comment is tangential]
I have always been empathetic to the argument, from people first presented with this, that they are different. Understanding how math deals with infinity basically requires having the mathematical structure supporting it already known. I’m not particularly gifted at math, but the first 4 weeks of real analysis really changed the way I think, because it was basically a condensed rapid upload of centuries of collaborative work from some of the smartest men to ever exist right into my brain.
Otherwise, at least in my experience, we operate in a discrete world that moves through time. So, what I predict is happening, is that when you ask that question to people their best approximation is a discrete world ticking through time.
Is 0.999...=1? Well, each tick of time another set of [0.0...9]’s is added, when the question is finally answered the time stops. You’re then left with some finite number [0.0..01]. In their mind it’s a discrete algo running through time.
The reality that it’s a limit that operates absent of time, instantaneously, is hard to grasp, because it took brilliant men centuries to figure out this profoundly unintuitive result. We understand it because we learned it.