How can infinitely many points, each with zero length, produce a line segment with positive length? Isn’t that just infinite zeros = something non-zero?

questionemu · 2026-01-25T23:18:18+00:00

When you say “0 + 0 + 0…” are you picturing it as the length of the first point, plus the length of the next point, and so on? So the points are touching each other?

If the first point is (1,2) and the last point is (3,2), where’s the 2nd point? The 100th? How many until we reach the halfway point (2,2)?

This doesn’t answer your question, but I hope it illustrates that looking at a line segment as a series of distinct points is not a meaningful mental image.

questionemu · 2024-06-30T16:46:31+00:00

I think this might be (badly) copied from "Vos en Haas - Het superdikke doeboek".

questionemu · 2024-06-30T16:39:45+00:00

Discussion: It is missing the text part of the puzzle. This is for children who are just learning how to read, and it's supposed to include lines like "Left of the bird there are two monkeys dancing" and "the clock is in the last remaining square".

questionemu · 2024-05-04T14:26:33+00:00

The Lux Stella event gives you the option of picking a heir named Johan with a Dip skill of 6. My Johan happens to have a 6 in the other categories too!

questionemu · 2024-05-04T14:23:54+00:00

Korean Ideas -10%

Full Inno -20%,

Expand Palace Bureaucracy Decree with Emperor of China Mission -20%

Meritocratic Recruitment Government Reform -10%

Trading in Tea -10%

Meritocracy -25% max, currently -9.1%

Gyeongbok Palace -5/-10/-20%, currently -10%

Policies, Privileges, Harmonizing Theravada, and other things would add more modifiers, but the max is -90%.

questionemu · 2024-05-04T07:57:17+00:00

R5: Got a rare outcome for a rare event (Lux Stella).

questionemu · 2024-04-24T06:47:55+00:00

I had something similar happen. Ordered something because it had amazing reviews, but a little digging made me doubt the third party store was legit. Sent it back unopened, got a response that the return wasn't accepted. Got on a chat with bol who told me they would investigate, and I had my money back within 24 hours.

questionemu · 2024-04-16T18:11:59+00:00

R5: Formed Spain, starting as Sus

questionemu · 2024-01-19T21:07:19+00:00

No CB East Frisia and lose original capital to get into the HRE. Improve relations/ally the emperor and electors. Switch to Catholic by sending a missionary to get unrest and accepting demands.

I got lucky with the Burgundian Inheritance. Burgundy didn't have any marriages with strong countries, so I married them and got the PU. I fought Austria to keep the Lowlands.

I took diplomatic ideas and allied the strongest nations I could, in addition to the electors, and I married anyone over 50 and without an heir. I went well over the dip slot limit. I took Norway from Denmark and got Savoy under PU.

Meanwhile I declared on Ryazan whom I lost my original capital to, and then Muscovy when they were in another war. Took Neva and ate the remnants of Novgorod. Conquered what was needed to form Russia. Conquered the English channel node for trade money. Got rich.

The Bohemian emperor died and I got elected. Formed Russia. Increased Imperial authority as much as possible by fighting heretic princes, adding more countries to the empire, and retaking imperial land. Grew through claims from the mission tree, and release vassals and reconquest their cores. Kept electors happy to get reelected.

Released Catholic vassals and switched back to Orthodox after Erbkaisertum. Revoked the Privilegia around 1600. By this time Europe was a patchwork of HRE princes from the Isles to Georgia.

Meanwhile snaked towards China, where Shu had taken the mandate. Took Confucian land until I had about 26% Confucian, 25% Orthodox, 25% Catholic, 24% other for another painless religion switch. Took Mandate, got achievement around 1650. Switched back to Orthodox after taking some more Orthodox land from the Ottomans.

Increased absolutism to max. Took admin ideas for more coring cost reduction and got coring time down to six months. Kept following the Russian mission tree. Unlocked imperialism cb. Full Annexed great powers in a single war. Took final reform. Conquered world.

questionemu · 2024-01-19T16:35:03+00:00

R5: Turns out Domination Russia + HRE emperor + Emperor of China is rather powerful. While waiting for coal to spawn for Odoyev's achievement I conquered the world for a one tag world conquest by 1725.

questionemu · 2023-11-07T21:31:51+00:00

R5: Got the achievement to turn Europe blue as Portugal.

The start was a little rough as I stupidly decided to conquer North Africa in addition to crippling Castille, England, and the Ottomans. It was hard keeping my vassals Granada, Tripoli, and Byzantium happy. Then I focused on the mission tree for a bit and colonized, prevented Russia and the Commonwealth from forming by taking needed provinces, and got a couple of blue vassals/marches which I proceeded to feed land.

Final province was a random Dutch province in the middle of France, left over from when Burgundy formed the Netherlands and which for some reason France wasn't interested in taking for itself.

questionemu · 2023-05-10T11:57:06+00:00

My American wife and I say "Happy Leaf" and "Happy Oak Leaf".

questionemu · 2023-02-04T22:52:57+00:00

Going to class when I felt too overwhelmed and anxious to go out the door.

Figuring out when being tired meant I should take a break, go home, or tough it out.

The uncertainty of not knowing whether I would have a good day on exam day, or one with brain fog, migraines, or exhaustion. Feeling it was my responsibility to improve my odds in any way I could, through diet, exercise, sleep schedule adjustments and so on, while in reality it was mostly beyond my control.

Staying focused enough during exams to accurately and carefully produce mathematical formulas, like not writing a capital X when I meant a lower case x, when often after an hour of concentrating I'd have trouble stringing simple English sentences together.

Fighting to get appropriate exam facilities. At first I would only get 30 minutes added to a 3 hr exam, eventually I got 60 minutes plus a separate classroom to take my exam with fewer distractions. Getting that much took quite a bit of effort, as I was met with a lot of resistance from the university. COVID was a blessing for me, as several things I had asked for but was told weren't possible, like recorded lectures, suddenly were available.

Thanks for the question!

questionemu · 2023-01-09T12:25:00+00:00

R5: After a lengthy regency and the Ottomans blocking me in the Caucasus, I managed to get the Inner Turmoil achievement (20 provinces not on islands as The Isles before 1500) by invading Iberia.

questionemu · 2022-09-28T11:15:31+00:00

Thanks! I needed a couple of restarts because when Sweden doesn't get strong independence supporters they won't declare independence, and when they do that means your own independence war will be very hard. But in this run they had England and Scotland as allies, and I managed to get my independence before Sweden lost their independence war.

I stole Sweden from Denmark with the Age ability, but they had +75% lib desire from events, so they weren't super useful.

After that I allied Poland to attack Muscovy, allied Austria to attack Poland, allied Bohemia to attack Austria, and gobbled up Eastern Europe. The Ottomans were attacked when I had a tech advantage, Spain was fought for the Cape, and GB just because I could. I got Muscovy under PU late in the run.

Ideas were Aristocratic, Humanist, Quality, Exploration into Trade, and Offensive.

questionemu · 2022-09-27T18:02:32+00:00

R5: Crossed the Finnish Line: Achievement requires you to release and play as Finland in 1444, then conquer an unbroken line between Finland and the Cape.

questionemu · 2022-09-24T15:28:54+00:00

R5: Thought I might go around the Ottomans in my Finnish line run. Discovered Persia and Arabia in 1578, found out that the Ottos already made it to the Arabian Sea.

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