Supertask, superchicken, paradox


In a recent thread, people were discussing "supertasks", and I
haven't completely caught on to what's going on.

Consider the following supertask.

Say we have a chicken which lays an egg, and when it does so,
it immediately pushes any other eggs in its nest, out of the nest.
Let's say it does this once every minute.

Then define f(n) = 0 if there are no eggs in the nest at time n,
and f(n) = 1 if there is at least one egg in the nest at time n.

Then for all n >= 1, f(n) = 1, so in the limit as n -> oo, f(n) -> 1

So from this, we might say that in the limit as n goes to infinity,
there is an egg in the nest.

However, the supertask experts seem to be saying that the
right way to think about the supertask is to number the eggs
1,2,3 ... oo, and then to argue that for all n, egg_n has been
removed from the nest, and hence in the limit as n goes to
infinity, the nest is empty.


So in the limit, is there one egg in the nest, or no eggs?

.

Relevant Pages

  • Re: Supertask, superchicken, paradox
    ... This is basically the same supertask. ... > it immediately pushes any other eggs in its nest, ... > and f= 1 if there is at least one egg in the nest at time n. ... is continuous at infinity. ...
    (sci.math)
  • Re: Supertask, superchicken, paradox
    ... > Consider the following supertask. ... > it immediately pushes any other eggs in its nest, ... > and f= 1 if there is at least one egg in the nest at time n. ... Thus function limfdoes not exist and for sequences ...
    (sci.math)
  • Re: Supertask, superchicken, paradox
    ... > Consider the following supertask. ... > there is an egg in the nest. ... > infinity, the nest is empty. ...
    (sci.math)
  • Re: Supertask, superchicken, paradox
    ... > Consider the following supertask. ... > it immediately pushes any other eggs in its nest, ... > infinity, the nest is empty. ...
    (sci.math)
  • The bird knows ???
    ... it was 13-year-old Alexa Rodriguez and not ... The hawk was perched on a railing in the upper deck behind home plate ... A single egg lay in the hawk's nearby nest in an overhang near the ...
    (alt.sports.baseball.bos-redsox)
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