On Dec 27, 2012, at 2:16 PM, kirby urner <kirby.urner@gmail.com> wrote:

Judge Hansen: Debater A wins because you can never have "infinity

triangles" i.e. 1/n approaches 0 as n->infinity but at no point is 1/n

actually 0, just as 0.999... is never 1 if you stop with the 9s at

some point. [Editor: "..." is one of the most magical of all symbols

in math, given what its allowed to do for us in our imaginations]

If you didn't understand then why didn't you just say so?

Do you understand that your contradiction is essentially between limit(n) * limit(720/n) as n->infinity and limit(n*720/n) as n->infinity?

Do you understand that the left side of that comparison is the part that is not valid, that limit(n) as n->infinity does not exist?

You may have meant something else, but you never stated the contradiction explicitly. You just said, how can these somethings go to zero yet if you add them all up they add up to 720. Translated to something explicit, that becomes limit(n) * limit(720/n) as n->infinity.

Bob Hansen