A real GIMPS math thought

[CRGreathouse]

Originally Posted by science_man_88

1/x=0 when x=

(1/x)*x = 1 if I remember correct.

0*x=1 ? doesn't seem to work out so it looks as though anything based in what I believe is called Peano arithmetic makes 1/ = 0 impossible.

Don't use rules from on objects not in it.

[R.D. Silverman]

Originally Posted by R.D. Silverman

That will teach me to try (too quickly!) to find a simple explanation
for something subtle. Obviously, I had a quaalude moment....

You are correct. They both go to zero. MAJOR Brain damage on my
part. For some reason, I was thinking about 1/[floor(x) - x)]...... Idiot

This is subtle...

Let me look at it again without invoking Euler-MacLauren summation.....

Everyone can award me the dunce-of-the-week award. The integral does
converge. Re-write it as:

limit a-->oo integral from 1 to a of (1/floor(x) - 1/x)dx

Call the kernel g(x). This is then:

limit a-->oo [ integral from 1 to 2 g(x)dx + integral 2 to 3 g(x) dx + ......+
integral a-1 to a g(x) dx]

What happens is that everything TELESCOPES...... It doesn't matter
that one winds up subtracting two infinite quantities. One winds up with
.

Major stupidity on my part.