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Inspired by the " special addition of velocity in special relativity " I came to consider this a long time ago.

Let x [X] y be the super of x [+] y.

[/] is inverse of [X].

Ex( L(x) [+] L(y) ) = x [X] y.

L is functional inverse of Ex.

Ex(x) = 1 [+] x [+] x [X] x [/] 2! [+] ...

is +,X,/,exp,ln the only solutions ?