Robert Hansen (RH) posted Jan 1, 2013 9:41 AM: > > On Dec 31, 2012, at 1:11 AM, GS Chandy > <firstname.lastname@example.org> wrote: > > > Of course, that student must arrive at a clear > understanding just how those repeating decimals 'go > to' the fractions 1/3 and 1/1 respectively. Given > this, the rest of RH's argument makes no sense at all > to me. > > That's because you didn't view the video. > > Bob Hansen > I have subsequently succeeded in viewing the video. I re-iterate my earlier argument.
To go by the evidence of my own case, the understanding of how a repeating decimal 'goes towards' infinity is a subtle idea that takes time to 'simmer' in the mind and 'come to a boil' - the 'moment of understanding of "infinity" as a concept' is almost an "EUREKA" moment (if I recall rightly). That 'moment' also goes on forever.
(I'm of course NOT claiming that I now understand infinity *fully*, or even as well as the best modern researchers into the subject - but I do know how to think about it so my head doesn't go into an impossible whirl.
(I also know how to use 'infinity' reasonably effectively in math, physics, etc; and to understand how others are using it.
(And also how to draw useful analogies and metaphors from it as and when needed.
(Of course, there is still an 'infinite amount' to learn).