So, I stole a page from Benjamin Baxter’s playbook and taught a lesson with the aid of comments from the Internet.
Specifically, in Pre-Calculus I was teaching the formula for an infinite geometric sum:
so is the first term and r is the number a term is multiplied by to get the next term.
For example, take .9999…, which is the same thing as
So and . Therefore .999… is
I looked at the posts from the .999…=1 saga at Polymathematics (check the sidebar) and picked choice excerpts from the comments, i.e.
My first reaction is that I am very worried if you are a maths teacher.
We read them over in class and discussed why the reaction to this problem would be so strong, and why so many people would doubt the mathematics.
One conclusion was that there’s an almost philosophical confusion here; an unwillingness to accept the mathematician’s version of infinity. Last semester I had my Pre-Calculus students write an essay on “do you think infinity exists in real life?” because I wanted them to wrestle the strangeness head-on. The abstract leap to the infinite and infinitesimals is really the crux of Calculus.
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