Date: Jan 1, 2013 3:09 PM
Author: Joe Niederberger
Subject: Re: A Point on Understanding

R. Hansen says:
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Sorry, I was asking for an example of what you are talking about that applies to 0.999...?
You wrote...
"It appears to me the "contradictions" as such surrounding these topics (be it .9999... or triangulations of a sphere) all are related to a very old debate regrading so-called "completed" or "actual" versus "potential" infinities."
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Example? Simply the fact that people often confuse what this notation represents - i.e., just as you say elsewhere, a limit, versus a process of forming the ever next term in the sequence .9, .99, .999, and so on. This leaves them with the feeling that the sequence can never quite equal 1 although it gets closer and closer. It appears that the process view somehow comes more naturally to people. Combine that with the fact that kids often hear about ".999... = 1" informally long before they ever study (if ever!) the modern concept of limit.

"Actual" versus "Potential" infinities form, as one Hall paper put it, "an ongoing fault line" through mathematical thinking. Its ramifications go far beyond limits, per se.

Double Cheer for New Year,
Joe N