Object A is 1.
Object B is 0.999...
A holds certain properties, i.e. "is a whole number", "is a single object", etc.
B holds certain properties, i.e. "is an infinite series of 9's following a decimal point", "is not a whole number", etc.
If two objects have properties which differ, those objects do not share an identity.
A (1) and B (0.999...) have properties which differ.
It follows that these objects do not share an identity.
Ergo, A =/= B.
Ergo, 1 =/= 0.999...