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With that in mind, what do you get when you add pi to itself? 2TT. Similarly, 0.333... added to itself is 2 x 0.333..., and not 0.666...
Now, depending on the requirements for the identity of TT to remain visible, I can simply say 4.283 instead of 2TT. So, by all means, take advantage of the fact the symbol for 1/3 happens to use numerals and do your arithmetic on them if you are willing to lose precision.
Well, add pi to pi and you can also get 6,2831... (in this context ... denotes all other digits in pi) and i won't lose precision. And you state that i will lose precision by equalling 1/3 with 0.333... (infinite number of 3's). I challenge you again to prove that last sentence.