Re: An uncountable countable set

Mike Kelly wrote:

Tony Orlow wrote:

it's not true that you can put ten balls in a vase and take one out,
over and over, and ever get an empty vase.

Because you can't physically perform an infinite sequence of operations
in finite time.

No. That's not the real reason. There are many mathematical models of
physical phenomena for which "an infinite sequence of operations in
finite time" is required, like e.g. in Zeno's paradox. The real reason
is that the infinity in the "balls in a vase" paradox is of a vastly
different nature: it cannot be understood as a limiting case of
something finite. It's a jump. And nature doesn't jump.

Han de Bruijn

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