> There is no proof that will ever satisfy a person dead-set against this.
Indeed. I've torn my hair out trying to convince smart people with PhDs in hard sciences and had to give up in frustration.
I usually find that the most success can be had by kicking the ball to them immediately and having them define what they actually mean when they say "0.999…". If we're going to debate whether that thing equals another thing, we better make sure we know what we're talking about. Inevitably, this either causes the dead-set person to give up, or give a myriad of definitions that are either meaningless, ill-defined, or causes them to realize that they don't actually know what "0.999…" means (or what they want it to mean). It is hard to have the patience to chase down the consequences of their ill-fated definitions, though.
Indeed. I've torn my hair out trying to convince smart people with PhDs in hard sciences and had to give up in frustration.
I usually find that the most success can be had by kicking the ball to them immediately and having them define what they actually mean when they say "0.999…". If we're going to debate whether that thing equals another thing, we better make sure we know what we're talking about. Inevitably, this either causes the dead-set person to give up, or give a myriad of definitions that are either meaningless, ill-defined, or causes them to realize that they don't actually know what "0.999…" means (or what they want it to mean). It is hard to have the patience to chase down the consequences of their ill-fated definitions, though.