This definition of identical as being ultimately dependent on Symbologies is just far far removed from what would be given to the word by any average speaker of the English language.
Which is why you should stop resting your entire argument on the assumption that this is the case.
Look, consider the following two individuals:
(a) George W. Bush
(b) The 43rd President of the United States
Are they identical? Yes or no?
Now, the
sequence of symbols "George W. Bush" and "The 43rd President of the United States" are not identical. But George W. Bush and the 43rd President of the United States
are identical, because identity is
not a matter of the symbols we use.
And exactly the same is true of 1 and 0.999...
The
symbols are different. But this has nothing to do with the question of whether the two things are identical.
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