Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/8/2024 1:55 PM, Alan Mackenzie wrote:

Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
 [ .... ]
 

When does an infinite process finally complete? If it does, well, it
was NOT infinite in any way shape, or form... Right?

 If an infinite process consists of an infinite number of steps, and each
step takes place instantaneously, it is instantly complete.

I can say all of the natural numbers. This does not imply that there is a largest one. So, an actual step-by-step process will never complete aka:
1, 1+1, 1+1+1, 1+1+1+1, ...
However, they are all there in instant, no time at all. Fair enough?

 An example of this is the construction of the "diagonal" non-member of a
purported complete list of real numbers expressed as decimals.  Each
digit of this non-member is constructed independently of all other such
digits.  So they can all be done "all at once".  The operation on a digit
takes no time.  Therefore the infinite process is instantaneous.
 If you had an infinite sequence of steps, where some steps depend on
previous steps, then picture the first step taking 1/2 second, the second
one 1/4 second, the third 1/8 second, and so on.  The total time taken
for this infinite process is 1 second.  This is like the race between
Achilles and the tortoise.