I'm not sure I entirely understand the proposal- does it change Inf aka ∞ ?
Otherwise I like it, and prefer the X::NegInf and X::PosInf,spellings as being easy-to-understand & a good Huffman-encoding. Before/AfterEverything are also easy to understand, and would be as natural to use for sorting strings, eg. for saying if a database NULL should go before the empty string or after everything else. On the other hand, if I'doing something with tangents and handling pi/2, I'd rather be thinking about PosInf as my exception and not AfterEverything. X::BE and X::AE are too short to use outside of this discussion, especially as "BE" is the common verb "be."