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?
>>17038398Sure. That doesn't mean literally every statement you can nake regarding it must pertain to the cone part.If someone told you their ice cream cone had sprunkles then do you imagine the sprinkles are literally embedded in the cone?A very silly world you must think you live in if this is how you interpret basic fucking English.
>>17038499Yes, if you say your ice cream cone has sprinkles on it, it ALWAYS means that the sprinkles are a feature of the cone, usually adhered to a rim that was dipped in a coating of e.g. chocolate; it NEVER means the sprinkles are a feature of the ice cream flavor itself; NEVER. Same as if you say you want salt on your margarita glass: it NEVER means you want the salt in the drink. Jesus fucking christ, anon.
>>17038519Idk, man. I just googled "ice cream cone with sprinkles" and it appears most of the results agree with my interpretation as opposed to yours.You're being very very silly right now.
>>17038525Idk man, what part of India did you google from? Like you're totally being le silly, man.
>>17038531I strongly suspect some form of trickery on your part, as evidenced by the row of thumbnails up top of your own image all showing the other interpretation. Just admit you are wrong and therefore inferior to me. It shouldn't be that difficult.
>>17038538>Indian debate syntaxKek, India confirmed. Next time poo in the loo and don't hide your search lol
>>17038541>don't hide your search lolAccept your inferiority.
>>17038543>search still hidden>brave browser confirmedkek
>>17038548All you needed to do to verify I'm using Brave is look at the filename in the first screenshot. But keep stacking those L's. It's funny.
>>17038553Oh, you don't say? Fucking lol
>>17038555Either way, I did quite enjoy derailing OP's dumbass thread with a heated debate about ice cream. Maybe we'll do it again some time
>>17038562
>>17038144>If p is prime>Checks p = non-prime >Arbitrary 2^(p-1) for no reason Stop gobbling ai slop. You're not doing anything useful. Worse you're harming yourself.
If the ice cream cone were divided by zero. Would the ice cream vanish or would the cone?
>>17038144This is why no one likes the maths guys and coders are working so hard to make them obsolete. Everything in your post and picture is boring as fuck and not exciting at all.
>>17038578you'll get infinite ice creams
>>17041995...zero size each
>>17038144A prime number has two distrint divisors, 1 and itself. That is the definition.This is why 1 is not a prime and 0 is not a prime. A midwit will say that 1 is divisible by 1 and itself and yet if we put the divisors in a set we must get a set of cardinality 2. If you put 1 or 0 twice in a set you still get cardinality of 1.This is why your definition of is sophistry.
>>17043674distinct*
>>17043674>>17043675A perfect number is a number where every number that divides it adds up to two times the number.
>>17043680[math]\begin{align}n &= \prod_{k} p_k^{a_k} \\2n &= \prod_{k}\left(\sum_{i=0}^{a_k} p_k^i \right)\end{align}[/math]
>>17043686Saw product instead of summation and tried to close my brain before more shit streamed in but unfortunately also saw the undefined k. I need to go poke my eyes out now and grill them in charcoal.
>>17043680The fuck are you on about?OP tried to first redefine primes then duct tape the broken definition to other concepts.Time to whip out the GPTs.. No prime can be perfect: By definition, a prime number's only proper divisor is 1. Since 1 can never equal the prime number itself (p > 1), no prime number can ever be perfect.
>>17043711>>17043686Uhhhh
>>17043792>>17043693try turning your brain back on, and you'll see why his equations are actually the answer to your proposal about perfect numbers. still in disbelief? try writing it out for some numbers.
>>17043793>>17043686
>>17043794Consider the number n = 120. Prime factorization is 2^3 * 3^1 * 5^1. The sum = (1 + 2^1 + 2^2 + 2^3) * (1 + 3^1) * (1 + 5^1) = 360. This is therefore not a perfect number. However the sum = 3n.I'll accept an apology now. It's not my fault you're too retarded to understand simple formulas.
>>17043797You're so dumb you can make stilllife cats appear to cry; wtf lol
>>17043798Apologize. https://math.stackexchange.com/questions/22721/is-there-a-formula-to-calculate-the-sum-of-all-proper-divisors-of-a-number
>>170381980 is prime because ZZ/(0) is integral and that's it
>>17038289yes
this is obviously bait and you all fell for it
>>17038152yes, please
>>17042404correct
>>17038144If your definition for any sort of "prime" numbers is almost exclusively odd numbers, your definition is completely fucking retarded
>>17045709nigger
>>17043798>>17043881you been real quiet. apologize.
>>17047979niggerread your own post again
>>17047986I did. I'm still right. Apologize.
