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Re: How teaching factors rather than multiplicand & multiplier confuses
kids!
Posted:
Nov 11, 2012 1:54 PM
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On 11/11/2012 7:16 AM, Joe Niederberger wrote:
> Excuse me, but I feel the need to clarify the post copied below. Clyde was saying his description of "zooming" and "convergence" (see below) was the "common sense view" of a continuous functions, to which I say WHAT?
>
> The common sense view of a continuous function is as I sate further below -- the graph of which I can draw without lifting the pencil. I think the conversion of that intuitive view into a definition involving limits was a great achievement for mathematics, and took some time to hit upon, nothing common sense about it. One must first struggle with Zeno's paradox to appreciate it.
>
> Joe N
But we should always check that our common sense is indeed sensible.
Consider the function:
F: y= x^2 if x is rational; -x^2 if x is irrational
Appears to be continuous at a single point (0,0) only. Can be drawn
without lifting the pencil - as long as the pencil stays still.
Gary Tupper
Terrace BC
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