Recent content by monikernemo

T162 RV - What was your plan for achieving the VC? What are the major steps you planned to take? What events, if any, changed the plan in execution and to what new plan? Any interesting decision points? Try to chain GAs, Work Ethic and get additional faith for each city converted to your...

They are answering a different question here. The classical question of squaring the circle (which means to construct a square with same area of circle via compass and straight-edge construction) is resolved and is deemed impossible. The question stated in the paper asks if you can cut a disk...

what do you mean by a `formal logic structure of Peano arithmetic'? This is true under the usual construction of the reals, either by Dedekind cut of rational numbers, or (equivalence class of) Cauchy sequences of rational numbers.

What the proof demonstrates is that given any enumeration of the interval, one can always produce an element that is different from all elements in the enumerations, and hence, there are no enumerations that exists.

The subtlety here is that some two numbers in the interval can have different representations in binary (i.e. trailing 1s, exists n such that for all m> n we have m-th digit to be 1 or trailing 0s) , so first one needs to fix a representation for all elements in A e.g. choose trailing 1s over...

Concretely one can think of binary representations as a map from a:N -> {0,1} with a(i) being the i-th number in the coefficient and the number a is denoted by a = sum a(i)2^-i. Now if a set S is countable, there exists a bijection between N -> A. Concretely, we can find an enumeration for...

Maybe if you can qualify what is a non-equivalent proof, and the original proof you had in mind? I find it disappointing as well that the asker is unwilling to fill in the logical gaps, after all maths is not a spectator sport. :P

(1) we assume law of excluded middle, so sets either contain or do not contain x. (2) we also assume standard ZFC axioms, so in particular, A is well-formed formula: A = {S in P(X): a in S} and B= {S in P(X): a not in S} And it's left as an exercise to figure out why A U B = P(X) and A, B are...

Sets are a blank canvas, and I don't think there is anything more one can derive from structure of sets. A method could be: Let A be subsets containing an element x and B be subsets not containing the element x. So there is an obvious bijection from A to B by f: A -> B with f(S) = S\{x} and g...

Not really, after all sets have very little to no structure.

The logarithm part can be refactored to: ln(x+iy+a)+ln(x+iy-a) Now suppose that a is fixed, and you take some suitable branch cut for ln (such that x+iy -a, x+iy-a is not in the domain)so ln(x+iy+a)+ln(x+iy-a) is holomorphic for this domain. In particular, if I am not wrong, you can find...

You are quoting me out of context. I'm talking about the early - mid game and not the late game.

kinda disagree. Might be more cost efficient to faith buy builders and chop.

Swordsman gets Oligarchy and Battering Ram bonuses, so I don't think Horseman warrants a nerf. This is why spearman need a buff or at least move Pikeman to somewhere more accessible. On top of that horseman gets 1 movement pillages which is ridiculous.

Yes certainly you get faith alongside work ethic, but I am comparing Oppidum to Hansas right now. At least in the early game, the more costly buildings are still Govt Plaza buildings. An earlier ancestral hall means faster expansion, which in my opinion seems more valuable than what Hansas can...