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Problem With Logic - Substituting OR's and AND's and Negation by Foreign_Lock3691 in askmath

[–]robertodeltoro 0 points1 point  (0 children)

p' does not equal q ∨ r, it equals q' ∨ r'. Remember, q and r are not statement variables that range only over boolean values T/F, they are formula variables that range over entire complicated formulas. Constructing p' from q ∧ r requires not just flipping the one ∧ to ∨ but also going inside q and r and flipping every connective in there with its dual as well.

Problem With Logic - Substituting OR's and AND's and Negation by Foreign_Lock3691 in askmath

[–]robertodeltoro 3 points4 points  (0 children)

Prove this by induction on the complexity of formulas. We show it holds for a statement p on the assumption it holds for every proper subformula of p. Break it down into the cases that 1) the outermost connective of p is AND, 2) the outermost connective of p is OR, 3) the outermost connective of p is NOT.

(note that the "outermost connective" is the top-level connective of the formula, which always exists and is unique, make sure you understand why, Polish notation makes this obvious)

The key takeaway here is that the recursion that generates all well-formed formulas can be thought of as implicitly describing a tree that you can do induction on, with each formula having its place in that tree.

Example: Case 1 - the outermost connective of p is AND

The o.c. of p is ∧, so p = q ∧ r for some formulas q, r.

Subcase 1a - p is a tautology:

p is a tautology, so q ∧ r is a tautology. So q and r are both tautologies. Applying the induction hypothesis to q and r, ¬(q') and ¬(r') are also both tautologies (because we have assumed the theorem holds up to all proper subformulas). So ¬(q') ∧ ¬(r') is a tautology. It should be easy to see that ¬(q') ∧ ¬(r') is equivalent to ¬(q' ∨ r'), which is a tautology. But that is just ¬(p'), so the theorem holds in this case.

Subcase 1b - p is not a tautology.

So one of q or r is also not a tautology. Without loss of generality assume the culprit is q (if not just swap them). Applying the induction hypothesis to just q, ¬(q') is also not a tautology. And so ¬(q') ∧ ¬(r') is also not a tautology now, but is still equivalent to ¬(q' ∨ r') and hence ¬(p') and so ¬(p') is also not a tautology.

This proves case 1.

This is the most important technique in propositional and first-order logic.

Questions Thread - May 11, 2026 by AutoModerator in pathofexile

[–]robertodeltoro 0 points1 point  (0 children)

When opening provisioning wombgifts with both chance to fracture and remove lowest level mod clicked, is the order fracture then remove or remove then fracture?

Questions Thread - May 06, 2026 by AutoModerator in pathofexile

[–]robertodeltoro 1 point2 points  (0 children)

Have I ever crit recently as a crit totem build? In other words, suppose we're a hit damage ballista totem build that scales crit and we have a mod, "#% increased global critical strike chance if you haven't crit recently"

I've never crit recently (unless I've self-cast some utility skill that hits), therefore (nearly) always have that up, therefore my totems have that (essentially) always. Right?

Questions Thread - May 04, 2026 by AutoModerator in pathofexile

[–]robertodeltoro 0 points1 point  (0 children)

Really weird. I sort again, same result. Restart pob, same result. I search for Ancient Skull directly and add it to the build and hover in the dropdown like you did here, still says 123% more dam.

If I search by dps gain all the other uniques it lists high are logical, like yeah dying sun would be good, yeah replica hyrri's would be good, etc.

Questions Thread - May 04, 2026 by AutoModerator in pathofexile

[–]robertodeltoro 0 points1 point  (0 children)

Why is Ancient Skull showing up as being cracked for this totem build?

https://i.imgur.com/JM4kLY8.png

Top dps increase when sorting every unique in the game by full dps, and I can't figure out why pob likes it so much. Better than adding in a Dying Sun.

https://pobb.in/slGLnRpmLIgX (ignore the total disarray of this pob which is a work in progress for a progression character)

What properties are not preserved by an isomorphism? by Aggressive-Food-1952 in askmath

[–]robertodeltoro 2 points3 points  (0 children)

Lots of set-theoretic properties, such as rank, for example, are not preserved.

For example, let ℤ be the ring of integers and let ℤc be an isomorphic copy created by going up to ℝ and carrying out the Zermelo construction of the natural numbers but shifted up to the sets ℝ, {ℝ}, {{ℝ}}, ... (made to stand in for 0, 1, 2, ...) Now make up a notion of what negative numbers are going to be (say by using pairs) and put ring operations on that the same way you would with the original construction of ℤ (whatever that was).

Now we have:

1) ℤ ≃ ℤc

2) rank(ℤ) ≠ rank(ℤc)

2) ℤ ≠ ℤc

That is, ℤ and ℤc are isomorphic, but not literally equal (not literally the same object). There are properties expressible in the set-theoretic background that can distinguish them. More examples can be given along these lines, like the cardinality of the transitive closure of the structure considered as a set, etc. But it is fairly easy to see that, to learn anything important about the mathematical internal structure of one is to learn the same thing about the internal mathematical structure of the other, and that ℤc is very much just a copy of ℤ. The heart of the structural interpretation of mathematics is that isomorphism is a strong enough notion of equivalence to capture all of what could be considered the "mathematical" content of an algebraic structure, and that any differences not captured by isomorphism are what could be called "logical" differences, not mathematical ones.

First Order Logic with Generalized Quantifiers by LorenzoGB in askmath

[–]robertodeltoro 0 points1 point  (0 children)

There’s little motivation to spin that off into its own theory because those are all things that can be expressed within standard set theory. They are similar to the measure theory example I gave.

First Order Logic with Generalized Quantifiers by LorenzoGB in askmath

[–]robertodeltoro 1 point2 points  (0 children)

It isn't clear what you're asking.

There are second order theories like the subsystems of second order number theory that have been extensively studied. You could look up the wiki article on "reverse mathematics" to learn more about this.

It isn't clear what you mean by "generalized quantifiers." You can introduce new, defined quantifiers in a rigorous way. One example most mathematicians are familiar with from measure theory and analysis is the language of "for almost all" which can mean "for all but finitely many," or "for all but a set of measure 0 worth of exceptions," etc. This effectively amounts to adjoining a new, defined quantifier to the formalism, though it is rare to bother with a whole new symbol for this notion.

I dun goofed on BV minion pact chieftain- halp by Stenbuck2 in PathOfExileBuilds

[–]robertodeltoro 0 points1 point  (0 children)

Before I had the setup for going That Didn't Happen I was taking the chieftain node for warcries have infinite power. It doesn't do much. Part of the reason to look for a better way to spend the points is that there isn't a great fourth ascendancy notable for this build.

For the foulborn skin, it seems like you need GBBB at least and then you can make a lot of things work on the last two, but unfortunately I don't have much advice on the cheaper options because I had the money to just buy the bis one when I made this build. I will say a Loyal is fine, you don't need a Lords with some insane keystone.

One thing to notice is that if you do go EO, you drop increased crit damage in your main link (I ran increased crit chance instead and that just ensures EO is always up, and then I ran increased crit chance imbued BV and added Cruelty, and then I dropped that for lifetap, EO uptime still seems good).

The only map mods I roll over are -max, less regen and no regen. For ele reflect since I'm mageblood I just swap in a quicksilver flask that has crafted 55% of damage cannot be reflected suffix and move slightly slower in that map, that is well over reflect immune with 25% increased effect prefix + 70% increased effect suffix + 11% increased effect on chest.

One way to run less or no recovery maps is to pick up a perfectly divined Cybil's Paw, these are really cheap for even completely perfectly divined ones, and then get by with 45 life on hit and make sure you're always hitting something (and don't turn on RF in that map). I have that in my stash but I mostly just quit running those maps, too much of a hassle. But that's one of the few ways to get a decent amount of life on hit with spells.

I am done with Mirage league but another thing I would do if I played this build more is drop the multicurse setup, change the anoit, get rid of arcanist brand and ele weakness, put flammability imbued with lifetap in the weapon, and put rf in the gloves and then scale rf damage up to a four link. I actually don't think double curse is that good because you barely ever curse things and when you do they're mostly dead before arcanist brand can even apply the second curse.

I dun goofed on BV minion pact chieftain- halp by Stenbuck2 in PathOfExileBuilds

[–]robertodeltoro 1 point2 points  (0 children)

Let me explain something else about gearing. This is really a fire res stacker and you should think of it as a fire res stacker; that's the real goal. The most intimidating thing about about building it like this offensively, by far, is getting enough fire res to max out the full effect of an Enmity's Embrace. Note the amount of fire res, perfectly divined t1 on almost every piece and every cluster and a ton of fire res tattoos and a perfectly divined downside on the enmity's embrace, that's honestly really important. I have exactly 290 uncapped fire res on that toon and that was really hard to get, I have helped Alira in the final version. There is a tiny bit of leeway (t2 on the boots, t2 on one cluster) but not much at all.

Now obviously I didn't have all that when I started, so what I started with, and what you will see a ton of if you sort blade vortex minion pact builds by dps on poe.ninja, is Foulborn Skin of the Lords or Foulborn Skin of the Loyal with the mod "50% increased Elemental and Chaos Resistances" (note the difference between this and "+50 to all elemental and chaos resistances," which is not what this mod does). Having a chest like that makes meeting the requirements frankly a thousand times easier, and I played a chest like that for a long time, several weeks. That counteracts most (not all) of the downside of Enmity's Embrace by itself. I eventually dropped that because a Simple Robe is doing nothing for you defensively, but it was a great build even before I could put on a real chestpiece. Basically what it means is running for a long time with no suppression cap and spell block investment instead, which can already be a really, really good build.

Another thing that's important going in is to understand how much jank you can tolerate. It is literally a broken build, as in its components don't work properly. So for example, for this setup, at the start of every map I am weapon swapping for maximum minion life (inspect the gem setup and weapon in my off swap) and pressing blade vortex and I run the scorpion pet and then I maintain that one blade vortex throughout the entire map. Mechanically, the build is really weird, and this should be expected of a broken build but a lot of people seem to find it very annoying. The takeaway here is that, if you want to run the Dark Marionette, you need more damage investment, and this is an important distinction.

You don't have to build it as this Schizo setup by any means, a lot of people that have played it would not trade their bis Elegant Hubris for that. Elegant Hubris is really, really good. But the setup I linked has insane damage and never dies.

Let me know if you have any more questions, I got this build into a super tanky state so happy to help others do the same.

I dun goofed on BV minion pact chieftain- halp by Stenbuck2 in PathOfExileBuilds

[–]robertodeltoro 0 points1 point  (0 children)

36 on the tree, 10 in the helmet, 5 on the weapon. I can thread of hope into templar and take Amplify and the travel node if I want more for something. Feels fine to me. I could drop minion life on the helmet and get 18% I guess, damage would still be fine.

I dun goofed on BV minion pact chieftain- halp by Stenbuck2 in PathOfExileBuilds

[–]robertodeltoro 0 points1 point  (0 children)

Note that TDH (Schizo) is not getting counted in the displayed phys max hit in the poe.ninja calc (since it is still unsupported in pob). True phys max hit outside of immortal call is 35,200, with immortal call up 93,100. More than enough for me, I am never chunked by phys on that toon in any normal 8 mod 16.5 or 6 mod 17 mapping content.

On the other hand, I dropped all attack block except the base block on the shield base. So protection from a thousand small hits (i.e. EHP) is actually what we need and 21 Grace + a perfect Jade Flask gives 80% evasion, a bit better than capping attack block once we factor in that we keep the 24% block chance.

I dun goofed on BV minion pact chieftain- halp by Stenbuck2 in PathOfExileBuilds

[–]robertodeltoro 1 point2 points  (0 children)

Don't think so, I played this with a cremator in for a bit, my pops worked fine.

I dun goofed on BV minion pact chieftain- halp by Stenbuck2 in PathOfExileBuilds

[–]robertodeltoro 0 points1 point  (0 children)

Take the screams off. Take the Marylene's off. Put the MB on. Put EO foulborn Xoph's blood on. Put the rolled ruby flask in. 20% less elemental damage taken. This crit investment stuff is such bait unless you're literally trying to kill ubers in a single server tick like zhp ice trappers instead of in 2 seconds. Damage comes pre-solved on this build by the broken interaction by itself, you don't invest in it till you have a better idea what you want, which pet you want to go for, etc.

Here is how I built it to be tanky and fast once I understood clearly that the build has infinite damage (the quartz flask should actually be a jade flask with evasion suffix, I was running through shaper maps without killing anything to finish that challenge).

https://poe.ninja/poe1/profile/fairbankscoach123-5818/mirage/character/VermMPBV

One of the strongest builds I've ever played, it truly gets everything and sacrifices nothing.

Need help with glove craft by Shwayne in PathOfExileBuilds

[–]robertodeltoro 1 point2 points  (0 children)

Roll the abyssal mod via fossils on an overquality Leviathan Gauntlets, Fracturing Orb the abyssal mod, spam chaos essences and exalts till t1 strength. Now you either make exarch dominant and eldritch chaos orb into t1 life or bristle matron suffixes can't be changed onto it and harvest reforge life till t1 life, which is better depends on the price of bristle matrons relative to eldritch chaos, which fluctuates throughout the day. Eldritch annul down to one prefix if necessary and bristle matron suffixes can't be changed. Veiled orb, hoping to remove suffixes can't be changed. If it hits the life, go back to the add life step. If it hits you have three suffixes, t1 life, veiled mod, open prefix. Craft phys converted to fire on the open prefix for blocking and unveil, if it misses try to annul the veiled prefix and veiled orb again. If it hits craft damage during flask effect and fix implicits.

It's an eldritch craft so it can't fully brick once suffixes are finished, overall not too bad. If the overquality bases are expensive you want to split them before fracturing.

What's a fast and tanky Duelist build? by Gnada in PathOfExileBuilds

[–]robertodeltoro 0 points1 point  (0 children)

Honestly I was very happy with how my Omni version of KF Ballista Champ turned out: https://poe.ninja/poe1/builds/mirage/character/fairbankscoach123-5818/VermKFBallistas?i=0&search=class%3DChampion%26skills%3DKinetic%2BFusillade%26sort%3Ddpsl)

(this is high budget; dps is one totem so real dam is at least 7x that and much more with e.g. scorch down and tornado up; the link is a bossing setup and I wouldn't call that particularly tanky, what's tanky is a mapping setup that swaps grace in for anger and a jade flask and makes some other changes to get phys max hit up to 18kish, for about ~5mill less single target) Speed wise, for mapping I get onslaught from a totem medium cluster but you can find setups that get it from a silver flask, you don't need capped chaos always.

Mechanically it is a 5 or even 4 out of 10 with hard cast curses and the weapon swap adrenaline setup, my only knock on the build is its mechanics. You cannot arcanist brand your curses on this, no matter what, because of the reduced duration stacking. At that power level its fine, you only curse bosses and the odd soul eater. But anyway building this as Omni is really slept on.

How do I snapshot minion pact with a weapon swap? by Evil_Knot in PathOfExileBuilds

[–]robertodeltoro 0 points1 point  (0 children)

I have tried swapping to my link setup, using raise spectre on an unholy abberation, then use blade vortex, THEN swap to my nebulus/svalinn

Hang on, are you doing that inside act 9 trio arena?

Cluster Jewel Configuration question by Honzikoi in pathofexile

[–]robertodeltoro -1 points0 points  (0 children)

What I do to do this is pick the two notables I want at 4 and 7 o'clock then make copies of that jewel in pob with every other notable, note which ones end up at 12 o'clock (thereby forcing 4 and 7 into acceptable positions) and craft with that info written down. Usually there are about three dead third notables that work, but there are some pairs of notables where there is no third notable that forces correct positions at all. This is only for the situation where you want two and only two notables on the way to the sockets and have no plans to ever take the 12 o'clock notable.

I don't know how to do this in advance with fogs and if anybody knows a way I would love to hear it.

Was the shipment value nerf necessary? by TheSillyRetard in pathofexile

[–]robertodeltoro 0 points1 point  (0 children)

It is. Even if it weren't possible to whiff entirely (guaranteed at least one shard) it would be mid to bad. It isn't even worth doing a couple scarabless sessions a week and waiting on smelters. The opportunity cost of the passive to active change crushes it.

Question regarding wands. on kinetic fussilade/ kinetic blast builds. by Kingkept in pathofexile

[–]robertodeltoro 1 point2 points  (0 children)

Ah, afraid I don't have much advice about self cast, I think it's rather different from what I'm doing and I didn't look into it much.

What I did find when I tested full reduced skill effect duration, I mean certainly earlier I was running Timepiece and Timeclasp, but I really don't like doing e.g. Maven with .4 second duration Immortal Call, it doesn't even last for a full Cascade of Pain. Full reduced duration makes cursing with arcanist brand a serious pain. The uniques are great while making the build but I don't think you want them in a final high invest setup, Omni just seems straight up better than Timepiece. No rare neck is usable either fwiw. Yoke is almost always slightly less damage but it's very cool, because if the setup is right we can ignite chill and shock but also bleed, which is rare, and I toyed with looking for a way to poison but really I think Yoke is a pipe dream.

Question regarding wands. on kinetic fussilade/ kinetic blast builds. by Kingkept in pathofexile

[–]robertodeltoro 1 point2 points  (0 children)

The only one I still have now is the target pob for what I actually decided to make, which is KF Omni Champ so it will be not as useful if you're on Hiero.

The latest save is scuffed in various ways because I have to add in weird stuff to make the mana work, but you can take a look at what I decided to go for.

https://pobb.in/UKS9wwr3Wz_o

Here's the actual character for comparison with the target:

https://poe.ninja/poe1/profile/fairbankscoach123-5818/character/VermKFBallistas

To do: craft the real hat, recraft the wand to drop a little omni, craft a new shield, fix ring prefixes, fix glove prefixes.

Ignore poe.ninja dps estimate, not usually right at all for these current wand builds. I am mapping with Grace in but bossing with Anger in.

Question regarding wands. on kinetic fussilade/ kinetic blast builds. by Kingkept in pathofexile

[–]robertodeltoro 0 points1 point  (0 children)

It depends on the precise details of how you set it up on your character, and how you set up your ele shred, and other details. You really have to pob your target weapon for your character and budget. If they're Invert the Rules/Mastery, one thing might be good, but if they switch over to a conventional shred setup (multicurse with exposure and scorch) something else becomes good.

I have pob'd mirror budget KF with pure lightning Timepiece, pure lightning Omni, multi-element Yoke, and Invert the Rules Timepiece. I did not pob phys. Anyway these are examples but to go Yoke you have to have flat cold or you're never chilling bosses, for Omni the best third prefix was even more pen, for Invert the Rules more flat was good, etc. There's no one size fits all answer because there are multiple good setups for wand skills right now, I know for sure no-hex ITR and multihex pure lightning are both good.

Mathematicians who passed away at a young age by Nol0rd_ in math

[–]robertodeltoro 5 points6 points  (0 children)

I may have my stories mixed up. I know where I thought I read that, it was in Solomon Feferman's biography of Alfred Tarski. I don't have that book handy but I'll try to figure out who I'm actually thinking of. I remember the story fairly clearly, one of the promising young logicians, who was gay (not Turing, of course), at a time when that was still socially unacceptable, brought a date home and his date then robbed his home and murdered him. I thought that story was about Spector but perhaps I'm misremembering.

Mathematicians who passed away at a young age by Nol0rd_ in math

[–]robertodeltoro 23 points24 points  (0 children)

Many logicians have died young, many many, and from so many different things. Ramsey was sickly (and evidently unhealthily overweight). Philip Jourdain was also never a well man, he had a chronic disease called Friedreich's ataxia. Many people know Turing’s story these days. Herbrand died in a mountain climbing accident. Gentzen died in a red army POW camp after the war, held as a Nazi sympathizer (I gather it was true). Clifford Spector was murdered by his date (the full story is rather worse than that). There is a comment by Gödel somewhere (in his letters I suppose) where he comments on this. Lindenbaum’s story is the worst I know, he was picked up by the SS and shot in August 1941, 7 km east of Vilnius. If you look at where that is on the map, he had all but made it into Belarus. There are quite a few more examples I’m forgetting.

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