# Re: Seven Step Series

```Bruno,
I am indeed ready to pursue further and since we'll be covering
both topics anyhow, I would prefer that you choose which would be the most
natural next step for us.```
```
Also, I assume you have seen the following and I wondered if it
tends to confirm UDA.

----- Original Message -----
From: Bruno Marchal
Sent: Sunday, July 26, 2009 11:38 AM
Subject: Re: Seven Step Series

I ask to all those who told me they were happy that I pursue this little
teaching further the following question.  Are you ready that I pursue? Are you
ready that I introduce a few bit of "new" material. Sometimes (actually most of
the time) new materials can shed new light on what has been already seen.

What do you prefer, that I continue with the sets (with the notion of
couples, and then of cartesian products, and then of operation, relation,
function, etc.)
Or do you prefer I prove first that the square root of 2, you know, that
number which multiplied by itself gives 2, is irrational (= does not belongs to
Q, = is not a fraction,  = is not a periodic decimal). ?

I am sure many of you already know this, but this is an typical impossibility
result, and somehow the whole machine 'theology' is a collection of
impossibility results, so the irrationality of the square root of 2 is a good
introduction to such type of result. Also I will give you a typical example of
non constructive proof base on the square root of two. (And for those
interested in the quantum confirmation of comp, the square root of 2 is the
amplitude coefficient leading to the probability 1/2, which is rather
important, if only for examples again).

It is really like most prefer. You can tell me: "do like you want", but I

Bruno
http://iridia.ulb.ac.be/~marchal/

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