Re: An uncountable countable set


Virgil schrieb:

In article <1152639759.882706.252490@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Virgil schrieb:

The first edge is mapped on the first path.

Which of the infinitely many paths through that edge is the "first" one?

That at the root.

All paths start at the root.

There these all are one path. You may call it bunch of paths.


If this splits in two, 1/2 of the first edge in addition to the new
edge is mapped on the new paths.

You are not allowed to split edges. Besides which, the first edge has
already been entirely used up.

It is inherited by the childs of the first path.

Paths do not have children, only nodes have children.

Call it as you like. The first bunch splits in two bunches. These two
inherit half of the first edge each.


If the new paths split, 1/4 of the first edge and 1/2 of the
second and all of the third are mapped on each path. Do you know what a
geometric series is? What do you object to this mapping?

If one can split edges into infinitely many peices one can equally split
paths. it is only unsplit edges and unsplit paths that are to be matched
up in injections, surjection or bijections..

You dislike fractions in calculations? Several thousand years ago
humans discovered that fraction can be useful. Why should they not be
useful in set theory?

Some things are indivisible. An edge must start at one (parent) node and
end at another (child) node. Any proper fraction of one won't reach.

We do not consider its function here, but its value of 1 edge.

In the set of naturals {} is the first.
What does half of {} mean? Or any other fractional part of {}?

In the set of naturals 1 is the first. The first edge is one edge, not
{} edge.
However, one edge is the first one, and this first one is divided in
two halves.

Regards, WM

.

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