Re: Attempts to Refute Cantor's Uncountability Proof?

Nathan wrote:

Hatto von Aquitanien wrote:
Nathan wrote:

You're supposed to learn to understand the meaning of
the limit of a sequence, particularly the idea of the sum of an
infinite series as the limit of the sequence of partial sums.

Not everybody does learn to understand this, which explains the
.999...=1 threads.

Is that what happens to all the smart people in college? They have their
common sense psychologically pounded out of them. They either give lip
service to the orthodox canon, accept it as truth, or transfer to
computer science.

No, there's another option you left out; the one I gave.
They can also learn to understand the concept of a limit.
As I said, this is what is supposed to happen.
This doesn't require that they "accept it as truth", as some sort of
dogma.

There may indeed be those who "give lip service to the canon",
because they really don't grasp it. There certainly are those who
"accept it as truth"; it can be very hard to help certain students
to learn to understand concepts and not just to do mechanical
calculations. Some in that category do transfer to
computer science, where they still tend to have trouble
understanding concepts.

And no, this doesn't necessarily happen in college. I said
"around the second semester of calculus", which for a lot of
"the smart people" means in high school.

Perhaps you can explain to me how one arrives at 1/3 = .333... without
appeal to an iterative process extended ad infinitum.
--
Nil conscire sibi
.

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