Darn, composed for too long and my service provider killed the connection.
I will agree that within a hypothetical convention where infinity exists 1 = 0.9 recurring. I would also argue that using the natural numbers as a convention the numbers 0 and recurring decimals 9’s don’t exist to have equivalence.
It is a matter of convention and not all conventions are created equal. Yet it is a postulate that .9 recurring using an infinite convention is equal to 1 limited by another convention of the infinite. Different sets that are not inclusive.
We “let” it be equal in an infinite set as an axiom, while it doesn’t exist within the convention of natural numbers as other example of an infinite set. We have already determined all infinite sets aren’t created equal such that a .9 recurring in a set does not require it be equal to a 1 from every other case of an infinite set. 1 can not be equal to .9 recurring in a set that does not include .9 recurring as a member of it’s set.
It is presented as a one or the other case while there is an “and” option in place of “either/or”. Just what exactly are we “letting” the unequal non-equivalent sets include axiomatically?
OK. this ‘seems’ to “sum” up the argument as reasoning thus far. (don’t know, could be other members of an infinite set, axiomatically). I don’t know maybe the first draft was a member from a set that was a more accurate representation. What are we going to “let” axiomatically?