Re: Why does everyone do it?

On Aug 20, 5:12 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
[...]

Yes. The above is precisely what I've figured out yesterday evening,
inluding the pictures. I cannot improve on your explanation.

Great! So half of your brain is working.

This has been my response to Tonico in a previous posting:

Well, Tonico, _one_ of my brain halves _does_ indeed understand that:

lim{n->infinity} f_n(x) = 0 for every x
and therefore a zero outcome for the integral.

But not the other brain half. This is a typical example of how limits
are being mis-used with mainstream mathematics. If you go back to the
finite domain for a moment, then it's easily spotted what goes wrong.

That's what I say. In my philosophy, there must be a way _back_ to the
finite domain, for mathematics to be relevant. So the above mathematics
may be "true", but it's irrelevant. With  lim{n->infinity} f_n(x) = 0 ,
information is lost irreversibly. And there's no way back .. to earth.

This seems to be the other half of your brain talking. And, uh, it's
turned off!! What do you mean "information is lost irreversibly"? Of
course in a limiting process information is lost irretrievably. That's
the proce you pay for simplifying.

lim{n->infinity} 1/n = lim{n->infinity} 1/n^2 = 0. Once you work with
the limit, you have discarded the information of how you got there. So
what?

The example I gave you is actually from physics: A wave is traveling
from left to right, losslessly. There is not force to destroy the
wave, so its energy persists. Yet for every point along the path, once
the wave has passed, there is calm. I really don't get what is so
difficult or threatening or even counterintuitive about this.
.

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