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Topic: Matheology § 288
Replies: 160   Last Post: Jun 21, 2013 8:42 AM

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 LudovicoVan Posts: 4,165 From: London Registered: 2/8/08
Re: Matheology § 288
Posted: Jun 18, 2013 10:32 AM

"apoorv" <skjshr@gmail.com> wrote in message

> Suppose we draw up triangles
> ...............................l..
> ...........................1....1
> ........................1....1....1
> .....................1....1....1....1
> ....................................................
> ...........................................................
> 1....1....1....1....1....1....1....1....1....1....1....1
>
> Each of the diagonal is of the order type {1,2,3....w}

That would be w+1, the order type of N* := {1,2,3,...} U {w}.

> The question is what is the order type of the bottom horizontal line?

Consider this:

1-> 1
2-> 12
3-> 123
...
n-> 123...n
...
___
w-> 123...n...___w

The order type of the w-th entry is again w+1.

So, the "triangle" is "equilateral", at every step as in the limit.

There just seems to be a sort of dissymmetry, so that the n-th entry has
order type n but the w-th entry has order type w+1. But I guess this is
simply because we are overloading the symbol w. To sort it out, maybe
something looking like the following would work?

Let w* := w+1 be the order type of N* := N U {w*}.

Then we would rather write the bottom line line as:

w*-> 123...n...___w*

and the w*-th entry would indeed have order type w*.

Otherwise, how to make head or tails of that "dissymmetry"?

Julio

Date Subject Author
6/14/13 mueckenh@rz.fh-augsburg.de
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