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WM <wolfgang.mueckenheim@tha.de> wrote:
It is the concept of number of elements. It is appropriate in actual infinity.No, even an unbounded sequence does not get longer when shifted by one step.The concept of "length" appropriate for finite sets doesn't apply to
infinite sets.
infinite means "without end" - unendlich.Actual infinity means complete. That implies a fixed number.
Fixed means that no element can be added and no element can be lost. The number of nines is fixed. That is an assumption only, but necessary for bijections.You don't understand that actual infinity is a fixed quantity.It may be "fixed" whatever that might mean, but to regard it as a
"quantity" is more than questionable.
It also means surjectivity. The preimage is complete by definition.Bijection means completeness.No. Bijection just means a 1-1 correspondence between the elements of
two sets. > Nowhere in that definition is any mention of completeness.
The diagonal number _is_ complete. Remember, we are not constructing itOnly when the set of indexes is complete.
tiringly one digit per second, or anything like that. The entire number
is defined and simply exists.
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