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'1' is referred to as a unit. I am not sure if there is a special name for '0' though.
There is no special term for such numbers.
Anything to the power of 0 is 1, apart from 0 or infinity, because they are just special numbers. :)
nothing goes into 0, and i don't think zero goes into anything else. 1 can go into everything but nothing can go into it
To start with, the identity element of multiplication is 1, that of addition is 0.