Where can I get a 7000 x 7000 JPEG printed?

Note that the 300dpi standard is based on conventional offset printing commonly run at a 150 line per inch screen. The DPI=2 x LPI rule really only ‘works’ for halftoned images. Since inkjets and giclees (which is French for ‘inkjet with more markup’) use a screening technology more akin to stochastic (but with the added fun of variable droplets), the formula isn’t so concrete. In fact, there’s a lot of debate still about what resolution is actually necessary, compounded by the sekrit image processing stuff that the inkjet driver and hardware does to your image during printing.

Some people will tell you that your standard 1400ish dpi inkjet needs 360ppi input for best quality. Others place that number at closer to 240ppi. I lean toward the latter figure. I have also found that when necessary, as low as 150ppi works fine with most inkjets, particularly when we’re doing wall-sized stuff that will be viewed from more than a couple of feet away. The nice thing about inkjet technology is that it deals with low-resolution sources so much more gently than the halftone process.

http://www.inkjetworkshop.com/faq.html
http://photo.net/bboard/q-and-a-fetch-msg?msg_id=000QQq

Since forever.