Two symmetric measurements may cause an unforeseen effect

Abstract

We may try to discuss gently the fact of "symmetric measurements outcomes" that is free from the order of measurements themselves, which fact might be extended to considering naturally the uncertainty principle. For two symmetric measurement outcomes, sometimes, the two measured observables are commutative. In this specific and symmetric example, we introduce a supposition that the operation Addition is equivalent to the operation Multiplication, and then, we may be apt to have an example of an inconsistency, probably due to the nature of Matrix theory based on non-commutativeness. We show here the inconsistency in an arbitrary dimensional unitary space when measuring commuting observables/an observable. We would say that the trial above might be categorized into an inconsistency example in the effect of the uncertainty principle, if we are forgiven for describing the above.