I'll start with your closing remark, then in sequence after that:
I am not brooding for a fight. And I respect your knowledge; almost surely, you know more about mathematics in general than I do.
Originally Posted by Deveno
No, I am not. I said MYSELF that there may be more elegant proofs. But my proof is clear.
i think you are confusing elegance with clarity.
It's quite clear.
your argument isn't very clear.
It makes sense at each step.
it makes sense, once it's unravelled,
I don't opine on that comparison. Of course my proof requires that one read it carefully, line by line, and with some understanding of certain modes of common mathematical reasoning.
but it places more of a demand on the reader than Sneaky's does.
Also, what exactly do you point to as Sneaky's proof?
It's hardly an "admission". There is nothing wrong with such quantification; indeed it is deft in this case.
by your own admission, you make an existential and universal quantification on the same variable, q.
It requires the reader to understand an argument of the form:
understanding WHY this is permissible (and not logically indefensible) makes QUITE a demand on a reader,
Suppose, for all q, Pq -> Rq.
It was earlier established that there is a q such that Sq.
So let Sq.
From Sq, Pq -> Rq, and other information, we show T.
So, if (for all q, Pq -> Rq) then T.
Inductions can be simple or extremely complicated. And the induction I did there was only a few lines.
especially for an induction proof, which are often quite elementary in nature.
All you had to do is read the proof carefully exactly as I wrote it. I explicity included the quantifiers "for all q" and "for some q". The reasoning itself (aside from the details of the arithmetic) is as basic as I just mentioned above.
in reading your proof for the first time, i had to go back and tell myself: "oh, he doesn't mean the same q in the same way HERE, as he does THERE".
I love it when someone is snide then when called on it says, "Oh, why do you have to take it personally?" I called you on your being snide. That's all.
you also seem to be reacting to this quite personally.
And vice versa. And I didn't conclude that you had much feeling about it; I just called your snideness, that's all, whether you have any feeling in it or not was not my real concern.
the fact is, i don't know you, and i certainly don't have any feelings about you one way or the other.
And please go to the top of this post, back to your own closing remark, which I appreciate, and my response again.