The Conqueror From a Dying Kingdom - Vol. 1 Ch. 3 - A Distant War

[MrGrinns]

J-Novel

Thats paid viewing. Im not invested enough to spend money just for a series that uploads so rarely

 

[koga88]

Just leaving a mention here that I appreciate you picking this back up and hope that you continue. Don't let that minuscule update from the previous group try to put you off of this if you really want to keep it up.

 

[DarksLight21]

Thats paid viewing. Im not invested enough to spend money just for a series that uploads so rarely

There's always pirate site where you can download the ebook if you don't want to pay.

 

[feha]

just a nerd passing by.
so what are they discussing on page 27-29 is basically something called "Euclid's theorem of infinity prime numbers"

so Saim is wondering if prime numbers would keep going because the way she saw it, the gap between prime number are keep getting wider and wider the further the number goes. and why the fuck a 5 years old girl would even pondering about such a thing? it's just a phase.

so the MC is basically explaining it like.

2x3x5+1=31
2x3x5x31+1=931

the formula is basically that you're multiplying any prime number that you know, and then add 1 to the sum of it. using this formula would resulting in either P or Q
P is basically means: if you get a prime number as the end result. then that means you're multiplying ALL of the prime number in the correct order, since 31 is a prime number that means you got all of the first 3 prime number correct in equation

Q is basically means: if the end number wasn't a prime, that means the divisible of the sum would show you the prime number that you missed. 931 isn't a prime number since it's divisible by 7, 19, 49, & 133. which 2 of them are prime number which wasn't part of the equation.

this formula weren't meant to solve anything, but by the construct of it this formula prove that you could ALWAYS find a new prime number as long as you multiply all of them and add it by 1. thus why it's called theorem of infinity prime number.

you can google it if you want a further explanation, but this is basically the gist of it.

Another nerd passing by~
Doesn't quite feel like that is what he is describing though.
Take a look at what he said:

• Let 'N' be a number equal or greater than 2
  • N and N+1 can't share any divisor > 1
• N*(N+1) = X
• M = "number of prime numbers" = infinity
• get_factors(M).filter(n=>is_prime(p)).length >= 2
  • -- unsure what get_factors is menat to do, but most likely it returns the list of prime-factors... except his added clause about counting the number of factors that are primes, as opposed to simply using the size directly, implies it isn't what he meant So maybe he means the list of all possible factors that could be used when factorizing? Like how "8" can be both "2x2x2" and "2x4" and "2x8", so get_factors(8) == [1,2,4]?
  • in other words, he states that the number of prime-factors in "infinity" is >= 2.
    • -- I'm sorry, what?
• assert( get_factors(M).filter(is_prime).length != get_factors(M).filter(is_prime).length )
  • -- I'm sorry, what?
• typeof(M*(M+1)) is Array && (M*(M+1)).filter(is_prime).length >= 3
  • or if we substitute M: typeof(infinity*(infinity+1)) is Array && (infinity*(infinity+1)).filter(is_prime).length >= 3
    • -- I'm sorry what?

The first and biggest issue is clearly when he defines M as infinity ("number of primes").
If we look at euclids theorem instead, we get this:

• Have an arbitrary (finite) list of primes defined through an arbitrary number "P" (which is the result from multiplying all primes in the list - aka the list of primes is "get_prime_factors(P)")
• Define q = P+1
  • if q is a prime: We prove that there is an additional prime outside of the initial set.
  • if q is not a prime: get_prime_factors(q) contains some prime-factor "p".
    • If this p were in our initial set: it would be able to divide both P and P+1, meaning p can also divide the difference "1" (which it can't). So this case is impossible.
    • But if p were not in the initial set ("assert(get_prime_factors(P).has(p))"): we have shown existence of a prime outside the initial set
• Since both cases proves the existence of a prime outside initial set, if we then repeat this algorithm ad-infinitum (adding p to the set each time: "P = P*p; Jump 0;"), we will infinitely prove the existence of new primes. Q.E.D

That's a very different proof, and clearly not what mc did.


All the above jokes aside though, I think it is fairly safe to say that either mangaka or tl did not understand the math, and they were in fact trying to put something like euclids theorem to paper.

 

[Maverun]

Thanks for new chapter

 

[Strela]

just a nerd passing by.
so what are they discussing on page 27-29 is basically something called "Euclid's theorem of infinity prime numbers"

so Saim is wondering if prime numbers would keep going because the way she saw it, the gap between prime number are keep getting wider and wider the further the number goes. and why the fuck a 5 years old girl would even pondering about such a thing? it's just a phase.

so the MC is basically explaining it like.

2x3x5+1=31
2x3x5x31+1=931

the formula is basically that you're multiplying any prime number that you know, and then add 1 to the sum of it. using this formula would resulting in either P or Q
P is basically means: if you get a prime number as the end result. then that means you're multiplying ALL of the prime number in the correct order, since 31 is a prime number that means you got all of the first 3 prime number correct in equation

Q is basically means: if the end number wasn't a prime, that means the divisible of the sum would show you the prime number that you missed. 931 isn't a prime number since it's divisible by 7, 19, 49, & 133. which 2 of them are prime number which wasn't part of the equation.

this formula weren't meant to solve anything, but by the construct of it this formula prove that you could ALWAYS find a new prime number as long as you multiply all of them and add it by 1. thus why it's called theorem of infinity prime number.

you can google it if you want a further explanation, but this is basically the gist of it.

W-what sorcery is this?
I could find a random prime number easily this way

 

[Beregorn]

Another nerd passing by~
Doesn't quite feel like that is what he is describing though.
Take a look at what he said:

• Let 'N' be a number equal or greater than 2
  • N and N+1 can't share any divisor > 1
• N*(N+1) = X
• M = "number of prime numbers" = infinity
• get_factors(M).filter(n=>is_prime).length >= 2
  • -- unsure what get_factors is menat to do, but most likely it returns the list of prime-factors... except his added clause about counting the number of factors that are primes, as opposed to simply using the size directly, implies it isn't what he meant So maybe he means the list of all possible factors that could be used when factorizing? Like how "8" can be both "2x2x2" and "2x4" and "2x8", so get_factors(8) == [1,2,4]?
  • in other words, he states that the number of prime-factors in "infinity" is >= 2.
    • -- I'm sorry, what?
• assert( get_factors(M).filter(is_prime).length != get_factors(M).filter(is_prime).length )
  • -- I'm sorry, what?
• typeof(M*(M+1)) is Array && (M*(M+1)).filter(is_prime).length >= 3
  • or if we substitute M: typeof(infinity*(infinity+1)) is Array && (infinity*(infinity+1)).filter(is_prime).length >= 3
    • -- I'm sorry what?

The first and biggest issue is clearly when he defines M as infinity ("number of primes").
If we look at euclids theorem instead, we get this:

• Have an arbitrary (finite) list of primes defined through an arbitrary number "P" (which is the result from multiplying all primes in the list - aka the list of primes is "get_prime_factors(P)")
• Define q = P+1
  • if q is a prime: We prove that there is an additional prime outside of the initial set.
  • if q is not a prime: get_prime_factors(q) contains some prime-factor "p".
    • If this p were in our initial set: it would be able to divide both P and P+1, meaning p can also divide the difference "1" (which it can't). So this case is impossible.
    • But if p were not in the initial set ("assert(get_prime_factors(P).has(p))"): we have shown existence of a prime outside the initial set
• Since both cases proves the existence of a prime outside initial set, if we then repeat this algorithm ad-infinitum (adding p to the set each time: "P = P*p; Jump 0;"), we will infinitely prove the existence of new primes. Q.E.D

That's a very different proof, and clearly not what mc did.


All the above jokes aside though, I think it is fairly safe to say that either mangaka or tl did not understand the math, and they were in fact trying to put something like euclids theorem to paper.

I mean, the first huge red flag was when he said "it would be strange if": at this point "it would be strange if" what you are reading is a proper mathematical demonstration...

 

[REDRED]

So essentially his uncle tried to set him up with his cousin?

Thanks for picking this up!

 

[feha]

I mean, the first huge red flag was when he said "it's unlikely": at this point "it's unlikely" that what you are reading is a proper mathematical demonstration...

Who said "unlikely" and when? I even went back to chapter to check, and can't find any occurence

 

[PS_Dane]

Thank god for full chapters

 

[Vinnaka]

Where, praytell might these translations be located?

Official English translation can be found on https://j-novel.club/
There are translating plenty of various kind novels

 

[Beregorn]

Who said "unlikely" and when? I even went back to chapter to check, and can't find any occurence

My mistake, replace "it's unlikely" with "it would be strange if", still the same result: the point is that mathematical demonstrations are absolute and not based on feelings or maybes.

 

[feha]

My mistake, replace "it's unlikely" with "it would be strange if", still the same result: the point is that mathematical demonstrations are absolute and not based on feelings or maybes.

That's not a maybe though. It is literally a statement saying that "it would be strange if" some assertion held true (basically: "this derives absurdity"). Using words like "strange" is not being uncertain.

As an aside, to showcase another example of such language: in Logic there's something called "proof by absurdity" (Reductio ad absurdum), which is how you can prove something by instead assuming the opposite and following that to its logical conclusion (when combined with other assumptions/axioms), and arriving at "absurdity" (Absurdity constant, ⊥, a literal possible value you can receive from logical operation, sometimes also called "contradiction", or simply "false"/"falsum").

Back on track, mathematics can likewise prove things in the same way (afterall, it is a branch of logics). An in fact, I did use that in my own example of euclids theorem, sort of (showed that p must be a new prime through how if it isn't we arrive at an impossibility - in other words, proved by contradiction). This is also likely what the mangaka tried to convey in their rendition of the theorem.

Fun fact, and TIL, is that Euclid's theorem is actually used as an actual example of "proof by contradiction" on wikipedia.

TL;DR
That's just his quirk of language. You will find many ppl using odd language/nomenclature in both mathematics and logics and other such fields. And that does in no way make their proofs invalid. Sometimes this terminology is even considered the conventional one. And sometimes it's just their own vocabulary, as they are using informal speech-language, maybe adapted to suit a recipient in an attempt at pedagogics.

 

[Demenster]

positive response

whats the source of your profile picture

 

[Rikurichi]

That's not a maybe though. It is literally a statement saying that "it would be strange if" some assertion held true (basically: "this derives absurdity"). Using words like "strange" is not being uncertain.

As an aside, to showcase another example of such language: in Logic there's something called "proof by absurdity" (Reductio ad absurdum), which is how you can prove something by instead assuming the opposite and following that to its logical conclusion (when combined with other assumptions/axioms), and arriving at "absurdity" (Absurdity constant, ⊥, a literal possible value you can receive from logical operation, sometimes also called "contradiction", or simply "false"/"falsum").

Back on track, mathematics can likewise prove things in the same way (afterall, it is a branch of logics). An in fact, I did use that in my own example of euclids theorem, sort of (showed that p must be a new prime through how if it isn't we arrive at an impossibility - in other words, proved by contradiction). This is also likely what the mangaka tried to convey in their rendition of the theorem.

Fun fact, and TIL, is that Euclid's theorem is actually used as an actual example of "proof by contradiction" on wikipedia.

TL;DR
That's just his quirk of language. You will find many ppl using odd language/nomenclature in both mathematics and logics and other such fields. And that does in no way make their proofs invalid. Sometimes this terminology is even considered the conventional one. And sometimes it's just their own vocabulary, as they are using informal speech-language, maybe adapted to suit a recipient in an attempt at pedagogics.

just to clarify, even though I'm the one who brought the topic up I don't understand any of this

 

[feha]

just to clarify, even though I'm the one who brought the topic up I don't understand any of this

Really? Which part? That people are allowed to use the word "would be strange if" (or any other non-ambiguous terminology) in their proof by contradiction? Or the tangent about formal logic and how I absolutely adore the fact that there's an "absurdity constant" (which you aim to derive during a proof by contradiction - named "proof by absurdity" in logic)?

Or were you being literal when you said "any" of that?

 

[kingdedede]

whats the source of your profile picture

pixiv 43852394

 

[coolkey]

Bro got that mathematician rizz

 

[ia_zero]

Future wife?

 

[Sp12er]

Ha, wife get! Now that's out of the way... What's this I hear about a war? It's a shame the releases are slow, it's a cool concept so far.

That's the main thing about this story,

Spoiler: Plotline so far

it's an mc that's living in a kingdom that's on its last leg, and he has no particular superpower other than his knowledge of modern earth.
Paired with a nationalist princess As a girlfriend, he tries to find any way to be safe with the people he loves.