While browsing The Paterek Manual, a book about framebuilding, I ran across this note, in a "supplement" at the rear (page 342):
Tube sets; Tange has recently introduced the Infinity series of
tubing. This is a seamed tubing that has tapered walls rather than butted
walls. During coldworking, the seams nearly disappear from sight and the
tube takes on almost the same strength properties as seamless tubing. Send
to Shimano for more information. The Infinity name comes from the concept
that the tubes do not have a starting or stopping point for the butt. In
effect, they are infinitely butted."
This book is not dated, but it looks like it was self-published, in the early 80s. I don't have a paper copy, just the scanned version that is available at http://icelord.net/bike/
What's interesting, apart from the technical claim made, is that this seems to be a "late-breaking news" addition to the basic text, which includes a chart with Tange tubing on the referenced page. That chart includes Prestige, along with Nos. 1 through 5. So, if all this can be believed, Infinity was not a precursor of Prestige, but was introduced later. The note in the supplement before this one advises of another tubing newly available from Tange: "900."