Not absolutely convergent series

All you faggots talking about 0.999~ = 1.

That's nowhere near the hardest thing to get your head round.

Take the alternating harmonic series.

1 - 1/2 + 1/3 - 1/4 .......
 
It's pretty simple to show it equals ln(2)

But if I re-arrange the order of the terms I can make it equal whatever the hell I want.

That's a mindfuck.

So for example

1 + 1/3 - 1/2 + 1/5 + 1/ - 1/4 ..... != 1 - 1/2 + 1/3 - 1/4 ...

even though the individual terms in them are exactly the same.

>>1
1 - 1/2 + 1/3 - 1/4 ...
This is a logical progression where the ``...'' is obvious.

1 + 1/3 - 1/2 + 1/5 + 1/ - 1/4 ...
This is not.