Re: Why does everyone do it?

Han de Bruijn wrote:
Tonico wrote:

On Aug 19, 5:41 pm, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:

Horand.Gassm...@xxxxxxxxxxxxxx wrote:

f_n(x) = 1 if n <= x < n+1
= 0 otherwise

Then int_{-infinity}^{+infinity} f_n(x)dx = 1, and hence
lim{n->infinity}[int...] = 1, as well, while
lim{n->infinity} f_n(x) = 0 for every x, and so

Huh ? That stumps me !

*************************************************************

Well Han, for someone that wrote just a couple of posts above that
"Uhm, as a theoretical physicist by education, I'm not _that_ bad
with (common) Calculus ...", you get stumped with very simple
stuff...

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.

No it isn't. It's a typical example of how the parts of your brain
have become (sadly) disconnected.

If you go back to the
finite domain for a moment, then it's easily spotted what goes wrong.

What _exactly_ does "the finite domain" mean? I don't find it in any
of my textbooks.

Brian Chandler

.

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