Actually, that might not be the case. . . While I was down at Headquarters I was looking at a LOT of badges and even when they used the members numbers that did not have anything to do with the chapter the chapter letter and such was all that was on the badge. I only saw 1 badge that had the A followed by four numbers and that was in a frame with other jewelry. This leads me to believe that it was a prototype or just a display piece - I could be wrong, though.
The badges I was looking at (with the exception of the one found in a frame with laveliers, recognition pins, rose bracelet, etc) all had the member's name, initiation chapter, and initiation date. This includes all those from the EARLY years of the fraternity (earliest one was 1907). We also didn't get up to members in the thousands for about 15 years at least - and by then the Alpha chapter was either gone or on its way.
Roses!
Sarah
P.S. Don't take this to mean that I think that this badge should be bought by just anyone. . . .