Hi Trippy.

In short, I am looking for a proof that achieves the unitary equivalence as the 'result' and not the 'starting' condition as inbuilt and inevitable via circuitous routes 'back to' that initially invoked/inbuilt unitary state. I hope that is clearer as to the difference between starting/predetermining with the unitary state and ending with the unitary state via a route independent of any staring unitary state conditions inherent from the get-go?

Cheers.

Would you care to elaborate on why you disagree? With specific reference to the point I made that the axioms as currently obtaining can only lead to "undefined" for the 0/0 construction? Can you explain where the mathematicians have any 'choice' in the matter if they apply said axioms as is?I disagree.

My mistake, yes. I already apologized, and explained that it was my assumption based on the fact that I already earlier and often effectively did address such questions on such trivial aspects ever before you asked them in that post. Again, I should have made clearer why I assumed them to be throwaway lines at the time. Again, my apologies if you were offended.That they were throw away lines is your assumption and your assumption only. They were legitimate questions I was using to illustrate a point.

Again, I should have made clearer what I meant. Namely, to invoke the unitary states when 'setting up' an exercise/proof is what I meant. That is different to the unitary state being the 'result' of that exercise, as distinct to being the circuitous inevitability of the exercise which had the unitary state built-in and the rest of the manipulations merely followed self-selecting logics from that setup unitary state.Do you understand how nonsensical this statement seems?

You want to prove that 0.999(9) = 1 without ever invoking a 1...

Take a moment to think about that.

In short, I am looking for a proof that achieves the unitary equivalence as the 'result' and not the 'starting' condition as inbuilt and inevitable via circuitous routes 'back to' that initially invoked/inbuilt unitary state. I hope that is clearer as to the difference between starting/predetermining with the unitary state and ending with the unitary state via a route independent of any staring unitary state conditions inherent from the get-go?

Cheers.

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