The oldest open problem in mathematics
N
̄ EU Math Circle, December 2, 2007, Oliver Knill
Perfect numbers
The integer n = 6 has the proper divisors 1, 2, 3. The sum of these divisors is 6, the number itself.
A natural number n for which the sum of proper divisors is n is called a perfect number. So, 6
is a perfect number.
All presently known perfect numbers are even. Here are the smallest 12 perfect numbers:
6, 28, 496, 8128, 33550336, 8589869056, 137438691328
2305843008139952128, 265845599156983174465469261595
191561942608236107294793378084
131640364585696483372397534604
144740111546645244279463731260
Whether there are odd perfect numbers is the oldest known open problem in mathematics: [10]:
Is there an odd perfect number?
Also unknow is the answer to the question:
Are there infinitely many perfect numbers?
We don't need to look past the number 6 in order to establish perfection in all numbers. This illusion of connecting our principles for mathematical coherence into subjective rationalizations for further expansion, inflation, exploration, parsing is invitation to denounce infinity as a summation of the realm for numerical data or usage. If we reflect on the notion first of proper divisors of 6 being 1, 2, 3 then it can be suggested that therein lies any basic formula for reaching the synchronized heights of elevated and imagined math substances from extensions of these divisors such that we omit all frequencies of patterns representing the climb or descent to these apexes or climaxes or perfection to the mathematician. Prediction is the basis for the concept of a perfect odd since we cannot see it yet we can objectify it as a conundrum to be satisfied by neutralized numbers between 6 and it. When we are discussing the evidence of a 1, 2, 3 or 6 we fail to adhere to the structural coincidences of all perceived realities- there is nothing which is not unique. A paradox to be sure since we cannot have a lack of anything without balancing it with the idea that there is no actuality to forms of duplicity. We are saying to access 1 by metering it in repetitions to get a 6. We can say the act of learning in our minds of a separation between a 1, 6 is to agree that suspended disbelief over our innate ideas that we know everything we do, we are, we see and we know is an origination against the previous instance of origination. Thus we may be able to devise a language for ourselves which is a binary sort such as 0,1 or 1, 2 that can explain our contingent understandings of learning. In order to sew a 6 from a 1, 2 and 3 we have summed up a separation of instances which clearly demonstrate the state of being for all involved to the acknowledgement so that we are agreeing to extract over and over again a product of uniqueness to organizational capacities which approximate functions, not other practical or identifiable forms of principal. We can say then we are left with 1, 1, 1, 1, 1, 1, etc. so that 1, 2, 3 becoming a 6 to be a perfect number instates the laborious entailment to inciting ourselves through redundancies for our denial that we know there is no separation to anything. If we imagine an invisible strand connecting infinitely to all which is within our universe then we are conquering the paradoxical liens against the freedom on our souls because we have found a way of connecting all numbers to each other as we see them! What has actually happened when we concede to the solution of a divided 6? If we use coherence to demonstrate the natural tendency of breaking sections of things off then identifying them by word or symbol, then we are still left with the idea that the division itself has not actually taken place, has taken place, continues to take place, stopped taking place and how we use it will be the parameters for the visage of the solution. Apples can be sliced up for example and it will always be apple, it's from the same apple, there's only two apple trees in Khazakstan which sourced nearly all sold apples in markets of the common world, the bits of the apples which fell created impossible to count pieces of apples from the slicing, the consumption of apples leads to processing as fuel then recycling to possibly become apples again. Without trying very hard, we have taken the idea of an apple being divided into the reproduction of itself from its own function as it relates to us. How often do we think about life for an apple and what that must be like?
We are seeing the beginning, end and sustenance of the basic illusion that productions of mathematica can resolve without any redress to instinctive bases for infinite comprehensions, that subdivisions are useful as media for interchangeable commodities up to a point it is impractical for daily enjoyment of survival, and that we are not at rest until we feel the master over nature which we consistently contradict ourselves is a Godly affair alone. To see a perfect odd, we must instigate a competition within our scientific collective to perfect infinity first.
No two things are alike, therefore no numbers past one can be proved except to demonstrate this formula.
1 = Infinity
DanaWanapskana
