I think that Microsoft is the sole authority on what B-Tree means in their systems, although like everyone else I learned that the "b" in b-tree stood for binary and find the use of the term a trifle misleading. However, the literature went to pains to explain the balanced tree and it's significance. To maintain that the MS-SQL 2005 indexes are binary tree indexes is incorrect. So yes, if they say b-tree in the context of MS-SQL means "balanced", it is pointless to argue otherwise.
I have no idea if Microsoft is the creator of "balanced indexes", and I certainly don't think they invented b-trees as you and I otherwise understand the term. This makes no difference to me, because they are not asserting that all b-trees are balanced trees. Again, this is strictly in the context of MS-SQL 2005. I haven't read the 2008 books, and for all I know they may be calling them BBQ tree indexes now.
Don't get me wrong. I understand why their use of the term is upsetting. But, I've actually noticed very little reference to the MS-SQL indexes as "b-tree" indexes. Usually they are simply referred to as indexes. But it's important to know that the indexes are NOT b-trees as the term is usually applied. That's why I agree that using that term at all is somewhat misleading, and it ought to be in BOL.
Finally, although it is off the subject, the connection of the term "PC" with IBM goes back to when IBM first introduced it's microcomputer. They named it the IBM Personal Computer. It was a branding thing. Although IBM wasn't the first to coin that phrase, other microcomputers like the TRS-80 weren't generally referred to as personal computers. The "PC" term came into general use meaning IBM or IBM-compatible as the IBM-PC and its clones (machines based on the Intel chipset running MS-DOS) came to dominate the marketplace. Gradually, that evolved into machines running Microsoft Windows. That's why Apple can run their "I'm a Mac... I'm a PC" commercials and everyone knows who they are gunning for. :-)
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