I understand the mathematical proof that 0.9r = 1 but I will never be convinced that the two are the same. We simplify 1/3 of 1 to 0.3r as it is impossible to represent it accurately.
Little point in continuing the discussion as I feel we are operating from different standpoints.
To summarise
Technically, 0.9r is not 1. Only 1 is one. The decimal representation of 1 is 1.0r.
1/Infinity represents an infinitesimal quantity, to use the term from earlier in the thread. It is approximately 0, but not equal to zero.
You can't say it equals zero because of the numerator; there is a 1 there, which denotes a quantity.
Don't get me wrong, I understand the reason that it is accepted that 0.9r equals 1, but in purely technical terms and precise math, it isn't truly equal.
You don't understand it then - mathematical proof is mathematical proof is mathematical proof - there is no 'technically' about it - it is likely your mistaken assumption that a non zero real number has a unique decimal representation that is throwing you off - it is the same number just represented differently.