No you can't. You can use Lossless JPEG instead, but regular JPEG (or JPEG2000) is a lossy format period.
edit: as tspiteri points out, JPEG 2000 does have a lossless mode. My bad. JPEG still does not though.
It's not, and the size of the file blows up to insane levels.
But then, if I save the second with a higher-than-otherwise-optimal setting, then I can reduce the compounding of effects. It's cost me filesize to limit loss to the imperceptible, but it's still possible.
You're right in practise (AFAIK, libjpeg still doesn't support this mode), but see http://en.wikipedia.org/wiki/Lossless_JPEG
> No you can't. You can use Lossless JPEG
The latter seems to be older and part of the original spec, while the former seems to be newer and a lot less bad.
And yes, LJPEG is the "complete crap" version which predates (and was blown away by) PNG, JPEG-LS is a second take on a lossless jpeg format.