Odd Perfect Numbers Shouldn't (Incomplete Proof v1)

[@abinitio_adinfinitum]

Point of Clarification: I am not claiming that σ(n) cannot contain a multiple of 2. IF I was, it would mean I am arguing that σ(n) cannot be even, but that is not the case given that the identity for both primes and perfect numbers in the sigma function are even, in other words primes (aside from 2) and perfect numbers always result in an even sigma sum. I am stating that the sigma sum σ(n) cannot be the even positive integer 2. If you're not convinced, grab a pen and piece of paper and start calculating σ(n) for all positive integers starting with the smallest positive integer of 1 and let me when you think you'll find a positive integer whose sum of divisors will add up to a total of 2. Go ahead...I'll wait ;)...shouldn't take long to understand what I'm claiming. (This post was inspired by a comment that claimed I was trying to say σ(n) can't contain a multiple of 2. (I think I know what my next video post will be about - a spotlight on the sum-of-divisors function)

[@nameless-yd6ko]

Something worth pondering might be that presenting something and claiming that it doesn't exist, is already prima facie evidence of it's existence! ;) Even 'infinity' exists! Wanna see it again; >>>> infinity. See?

[@abinitio_adinfinitum]

In a world without any constraints, you are correct. In fact σ(n) = 2 exists - just not for Positive Integers. Context is meaning. In this context, we are working within the constraints of Positive Integers, and have to abide by the rules that govern the positive integers. In this way our logical conclusions must be in accordance with the parameters of our system. Ignoring(or being ignorant of) the context of the environment leads to biased, subjective, arbitrary and even ludicrous conclusions. The truth would be whatever we wanted it to be. The entire exercise of studying Math and is usefulness is to be able to arrive at understanding (aka logical outcome).

[@nameless-yd6ko]

@@abinitio_adinfinitum Ahh, the bugaboo is in the constraints! With sufficient 'focus', much can be highlighted and much more can be ignored. Depending where you place the boundaries. The First Law of Soul Dynamics says; "For every Perspective, there is an equal and opposite Perspective!" And so with the Perspectives of 'possibility' and 'impossibility'. All 'meaning', like art and beauty and everything else, exists in the concepts/Mind of the beholder. Time can only be 'wasted' from certain Perspectives, opposite for others and a wide spectrum between.