Re: Tea cups and elephants

On Nov 28, 8:19 pm, Venkat Reddy <vred...@xxxxxxxxx> wrote:
I have posed this question in one my recent threads as a response to
some posts, but with no answer.

Constraint: Every tea cup has exactly zero elephants in it's contents.

Theorem: The cumulative contents of an infinite number of tea cups
will have a finite number of elephants in them.

Can this theorem be proven while meeting the given Constraint?.

- venkat

Without additional assumptions the theorem cannot be shown to be true
or false.

With appropriate additional assumptions. E.g.

The number of elephants in a set of tea cups is
the sum of the number of elephants in each tea cup in the set.

The sum of any number of zeros is zero.

the theorem can be shown to be false.

Note that for sets of points the second assumption is true, but the
first
assumption is false. The extent of a set of points may not be the sum
of
the extents of each point in the set.

The fact that each point has extent 0 and an infinite number of
points may have finite extent, is a simple result of measure theory.

- William Hughes
.