Perfect primes are primes with only 1 divisorusing (2^(p-1))((2^p)-1) and setting p as 0 and 1would yield 0 and 1.0 is the first even perfect prime number.1 is the only odd perfect prime number.continuing it would yield the rest of the perfect numbers, so wouldn't 0 and 1 be perfect numbers according to the equation without the exclusion? if the conjecture was if and only if it only has 1 divisor it is then perfect by definition. if the rule was set by man and not by math would that not break the entire case of mathematics being self-governing? Share your thoughts so I can feed my curiosity.
>>17038144Come again?
>>17038152Perfect number is a number who's divisor is its sum.Prime number is a number who's divisor is one and itself or two numbers.So by observation. A perfect prime number would be a number who's only divisor is itself .So 0 and 1 are perfect prime numbers.
>>17038159>Perfect number is a number who's divisor is its sum.No, start here.
>>17038144>IF random nonsense>AND more random nonsense>THEN absolute schizobabble with no rhyme or reason or any relation to anything whatsoeverBoy I love math
what's nonsense?1 is divisible by 1 and itself so prime number.1 is also a sum of 1 so perfect numbertherefore perfect prime numberI guess 0 isn't prime since you can't divide it by 1So maybe 0 is just a perfect number since adding 0 is just 0Not sure what you mean by nonsense since they already built an entire equation for it2^(p-1) * (2^p -1) and if you put the values in they really do make 0 and 1 as perfect numbers.
>>17038144>>17038159>>170381920 doesn't have only one divisor.It has only one non-divisor. Literally every number divides 0 except for 0 itself.>stop taking the schizo thread seriously!also 1 isn't prime either, because it's a unit, but that's somehow the less egregious thing going on here
>>17038198>0 doesn't have only one divisor.It has only one non-divisor. Literally every number divides 0 except for 0 itself.I guess zero is nothing then neither prime nor perfect.Why would zero not divide by zero? wouldn't that just be one since it divides by itself?>also 1 isn't prime either, because it's a unit, but that's somehow the less egregious thing going on hereThen 1 is a super perfect prime because it only has 1 as its divisor.
>>17038192See >>17038163
>>17038202Any number divided by itself = 10 divided by any number = 0Any number divided by zero is undefined. When you don't understand the foundations this just becomes a game of which "rule" takes priority. For the purposes of this discussion, the "no division by zero" always takes priority over any other rule at play.
>>17038242None of this matters; the divisors of a perfect number don't sum to it.
>>17038242Then would zero divided by zero be undefined or also zero? what rules are there in math? did someone just come up with it?
>>17038243What do you mean it does not sum to it? Does 1 not add up as 1 by itself?
>>17038245Perfect number doesn't do that.
>>17038247What does a perfect number do?
>>17038248Divisors sum to twice the number/
>>17038250(2^(p-1))((2^p)-1)What does this equation represent then if its not for classifying perfect numbers?
>>170382449 times out of 10, we're operating under ZFC set theory. Search that term up and you'll find pretty much all the foundational rules of modern math that most people follow.
>>17038255It does do that. Perfect number adds up to two times divisors.
>>17038257Perfect number has nothing to do with ZFC
>>17038259That wasn't the point I was responding to. (And technically it depends on your definition of "having to do with" but that's semantics)
>>17038260How does ZFC have anything "technical" to do with what a perfect number is? (Note that by intentionally adding the C to ZF, you've constrained the answer to be dependent on that axiom.)
>>17038264>by intentionally adding the C to ZF, you've constrained the answer to be dependent on that axiomIncorrect. Your premise is flawed. Inclusion of the axiom of choice makes the statement more inclusive, not exclusive. Evoking a system which includes the axiom of choice need not imply the thing I'm applying it to pertains to the axiom of choice.To answer your original question: the set of perfect numbers has to do with set theory in the sense that it is a set.
>>17038268Nope, specifying ZFC implies something about C, specifically; it's like ordering an "ice cream cone" >the set of perfect numbers has to do with set theory in the sense that it is a set.How is the ability to choose exactly one element from the set of perfect numbers germane to its construction?
>>17038258Is that technically the proof for what perfect numbers are? Why would an equation exist just to exclude what it tries to find?
>>17038277Exclude what?
>>17038268>To answer your original question: the set of perfect numbers has to do with set theory in the sense that it is a set.Does the equation define the set entirely?
>>17038280>Exclude what?0 and 1 as perfect numbers p_0 and p_1.
>>17038274>specifying ZFC implies something about C, specifically; it's like ordering an "ice cream cone"Wrong. You are imposing an arbitrary rule of language that only exists in your own mind. What I was doing was more like evoking UFC rules in a fighting competition and you're sperging about the rule in question also being in place in other combat leagues.
>>17038283What are the divisors of 1?>>17038284https://simple.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory
>>17038286>What are the divisors of 1?1
>>17038202>Then 1 is a super perfect prime because it only has 1 as its divisor....and dividing 1 means that it is a unit and thus not prime.
>>17038289What's the sum of 1? It's 1. Two times 1 is 2. So 1 can't be perfect number.
>>17038290>...and dividing 1 means that it is a unit and thus not prime.What would a unit mean in this context? Is it that it itself is the number that calls for units?
>>17038295a unit is anything which you can multiply by something to get 1. or, equivalently, something which divides 1in the naturals 1 is the only unitin the integers -1 is also a unitin the rationals, everything but 0 is a unit
>>17038292>What's the sum of 1? It's 1. Two times 1 is 2. So 1 can't be perfect number.So it has to be multiplied by 2? Then how is 6 a perfect number if 12 times 2 is 24?
>>17038300What are the divisors of 6?
>>17038292I don't think 2 is a divisor of 1
>>17038308See >>17038289
>>17038302>What are the divisors of 6?Are you not saying that (1+2+3+6+12)*2=24 is how a perfect number is found?After all you did 1*2=2 therefore 1 is not a perfect number so is 6
>>17038309Yes 1 is the divisor of 1.
>>1703831012 isn't a divisor of 6>>17038313What's the sum of 1?
>>17038286That wiki link does not make the point you think it makes.
>>17038315see >>17038308
>>17038317Sentence 3 restricts to S1; S1 doesn't restrict S3.
>>17038320Using a system that includes an axiom does not indicate that particular axiom is being evoked.
>>17038323It does when you append C to the standard ZF; exactly like ordering an "ice cream cone" evokes the cone, not just the ice cream.
>>17038319See >>17038289
>>17038329see >>17038308
>>17038331Do you see 2 here >>17038289
>>17038336Do you?
>>17038341No, do you?
>>17038345Then why are you asking?
>>17038347See>>17038310
>>17038349see >>17038292
>>17038358Where is 2 here? >>17038289
>>17038328If you order an ice cream cone, you can still reference the ice cream independently of the cone. This is just a laughably bad argument you're trying to make and I doubt you've even convinced yourself by it.
>>17038388Lol what. I wouldn't order an ice cream cone unless I were expecting a cone with my ice cream. Would you?
