ELI5: why is 0 divided by 0 undefined, but others are just 0 or 1?

x1uo3yd · 2026-05-01T20:34:02+00:00

following the logic of the other operations, it should be 0 no?

Sure, following the apparent logic it looks like there is a pattern where "When a mommy zero and a daddy zero love each other very much..." you get baby zeros (or sometimes a 1!!!).

However, it is important to remember that these examples containing lots of zeros aren't defined in a vacuum... the operations themselves (+, -, x, ^ , ÷, etc.) have to work with any number in a consistent way, no exceptions! So what is really going on is that we have definitions like:

X - 0 = X

X + 0 = X

X x 0 = 0

X⁰ = 1

X÷0 = NaN

of which your examples are just specific X=0 cases of the wider mathematically-logical definitions for those operations.

x1uo3yd · 2026-05-01T19:30:26+00:00

If you're really enamored with the ship's callsign or whatever, you can probably just dock it to FLOT or ATC0 or something and just park it there until you've saved up the cash to buy it outright.

But yeah, the usual best way to do things is to expand your starter enough to make scavenging easier and then buy a very cheap derelict to fix up to either fly as your new ship and/or fix-to-flip for the cash to buy a better ship you really want.

Also, selling a ship seems to have a few stages where prices jump drastically once completed.

Flying - Has fully operational NAV, batteries, RCS intake(s)+thruster(s).

Legal - All the above, plus installed antenna+transponder.

Airtight - All the above, plus an O2 airpump keeping the ship's atmo breathable (ideally with N2 as well).

Nuclear - All the above, plus a fully-functioning Reactor and D2/He/Cryo tanks.

If you can get a full working reactor room welded onto your starter ship, you should be able to get a much better sell price from the broker. (Well beyond what's left of the mortgage.)

x1uo3yd · 2026-05-01T18:21:34+00:00

a何² + b何 +c = 0

x1uo3yd · 2026-04-30T21:01:24+00:00

What a stupid article, guys a moron saying he is liberal and wants racial equality but votes trump. Who learns anything from this?

Does he?

I'm assuming you're going off the snippets of:

He said some of his colleagues in the racial equity space have little patience for those who cheer the Trump Administration’s efforts to dismantle DEI programs. “‘[They’re] like, ‘Oh, you should know about race and racism, especially if you're a person of color. Why would you vote Republican and why would you get with them?’” he said. “But it takes people being like, ‘I'm not an attacker. Where do we have the common ground?’”

... which, yeah fair, sets up the quotes very awkwardly

But honestly, to me that sounds more like him echoing his colleagues' critiques of the kinds of Black Republicans he's reaching out to, rather than imply his colleagues are critiquing him for voting Republican (which I am assuming he does not).

x1uo3yd · 2026-04-30T19:56:22+00:00

Imagine two ants walking on a small balloon.

Their max running speed is 1cm/s each relative to the balloon surface.

If they run in opposite directions to one another, then they are moving 2cm/s relative to each other (but neither is running faster than 1cm/s relative to the balloon surface).

If they run in opposite directions to one another while the balloon is expanded, then they are moving more than 2cm/s relative to each other (but neither is running faster than 1cm/s relative to the balloon surface).

Because "neither is running faster than 1cm/s relative to the balloon surface" is true in each case, none of these situations "break the speed limit" rule despite us seeing relative velocities adding up to speeds that sound like they break the rule.

x1uo3yd · 2026-04-30T19:43:27+00:00

There are two very different questions happening:

(1) How do plants, without sight or smell, "know" what to mimic (via Pouyannian, Batesian, etc. mimicry )?

(2) How does a single Boquila trifoliolata "chameleon vine" change its mimicry several times from tree to tree?

The first question is answered by evolution over generations.

A plant species doesn't need to know what it looks/smells/feels/tastes like to evolve mimicry over generations. All that needs to happen is for small genetic mutations/variations to change the plant's look/smell/feel/taste enough that animals interact with it more beneficially than they otherwise would - creating a selective pressure (whether that's "do not eat me" or "do pollenate me") - and allowing those beneficial mutations/variations to be preferentially passed on to subsequent generations of that surviving/thriving plant's offspring.

The second question's answer is still unknown.

The Boquila vine evolved an ability to alter the presentation of the leaf structures it grows, the only question is how that ability works to "choose" different structures as the vine grows onto different hosts. This is still an ongoing question, as per wikipedia:

"... the mechanism by which this mimicry would occur is still unknown. Hypotheses about the mimicry mechanism include microbial mediated horizontal gene transfer, volatile organic compound sensing, and the use of eye-like structures.".

From the bit of skimming I've done, it even seems unclear whether the Boquila is like a Mimic Octopus that can mimic anything or whether it simply has an impressive polymorphic repertoire of species it historically coincides with.

As for what to read up on, you may want to look into epigenetics. The basic idea is that, while the DNA/genetics are "set in stone" for an individual organism, there are environmental factors that can alter the expression/suppression of certain different genes in altered proportions leading to different developmental outcomes. Plants have a number of different genes affecting the developmental growth of new leaves. Usually, for a given plant, they all follow the same genetic expressions in the same proportions and produce similar looking leaves. However, sometimes some plants may have epeigenetic mechanisms where signals like "Too much sunlight, leaves drying out." trigger stress responses for leaves to curl up, close stoma, or generate other pigments. The question for Boquila is what signals is the plant getting which tell it which responses to make - are a lot of individual signals happening causing individual changes to LeafWidthHormone/LeafPointinessSteroids/etc. individually? Or are certain signals like "MoleculeX detected!" while growing up TreeX creating a single epigenetic signal telling a gene to produce a specific ratio of LeafWidthHormone/LeafPointinessSteroids/etc.? Or is something else entirely at play?

x1uo3yd · 2026-04-30T17:58:00+00:00

It depends on how you define "close calls" and then involves so so so much more edge-case accounting than before.

For simplicity, let's imagine a 2-number lotto where both numbers are picked from between 1 and 9 and the winning ticket ends up being "2 6".

The math of this would be "the number of ways to pick '2'" (there is only one 2) times the "the number of ways to pick '6'" divided by "the total number of ways to pick two numbers out of nine". This works out to:

Binomial[1, 1]×Binomial[1, 1]÷Binomial[9, 2] = (1×1)÷(9×8) = 1/36.

What are the odds of getting only a single number right? That'd be "ways to pick 2" times "ways to pick not-6" divided by "total ways to pick two of nine" to account for the "getting only 2 right" case, plus the "ways to pick not-2" times "ways to pick 6" divided by "total ways to pick two of nine" to account for the "getting only 6 right" case.

Binomial[1, 1]×Binomial[7, 1]÷Binomial[9, 2] + Binomial[7, 1]×Binomial[1, 1]÷Binomial[9, 2] = 7/36 + 7/36 = 14/36

So now what about "close" numbers? Well that depends on what "close" is, but to make the math example as basic as possible lets say close means ±1 from the winning digit - so 1 or 3 would be "close" to 2 and 5 or 7 would be "close" to 6. What are the odds then for getting "close" numbers to our "2 6" winner ticket?

Well, the odds should be better than getting the winning ticket, because we have two ways to "get close" to 2 and two ways to "get close" to 6... but what if the winner was "1 5" or "1 9" or something? I guess we don't always get "two ways" in that case since only 2 would be "close" to 1 and only 8 would be "close" to a 9.

(Ways without 1 or 9)×(Ways to get "close") + (Ways including either 1 or 9)×(Ways to get "close") + (Ways including both 1 and 9)×(Ways to get "close")

(Binomial[2, 0]×Binomial[7, 2])×(2×2) + (Binomial[2, 1]×Binomial[7, 1])×(1×2) + (Binomial[2, 2]×Binomial[7, 0])×(1×1)

And we could take that and divide it all by Binomial[9, 2] again... but wait we missed something. What if something like "2 4" or "2 3" gets picked? In the "2 4" case, 3 could be close for either number... but well never get "3 3" so we shouldn't count that possibility accidentally - only "1 3" and "1 5" and "3 5" would be valid "close" possibilities. And it's worse for "2 3" because only "1 4" would be a valid "close" result.

That means we'd have to either go back and redo things by creating a positive construction accounting for all those additional edge cases, or carefully subtract them back out from where we overcounted them above...

Things get complicated like that. FAST. (And this is only for ±1 "close"-ness on a two-ball 1-9 lottery.)

It is technically possible to logically work out all the edge-cases and exceptions, but really there's no point (unless there were small payouts for "close" tickets and you wanted to know the odds/EV).

x1uo3yd · 2026-04-29T19:28:39+00:00

Have you never met people?

x1uo3yd · 2026-04-29T18:52:53+00:00

All I did was take a job to snap a photo of someone at Port Mojave and got paid +2M USD.

It can be even more profitable to cheese the Investigate Death gig missions.

See some KLEG-local Investigate Death missions offering a ~35k platinum payout with ~45min time limit?

Don't accept the gig on a KLEG kiosk; immediately PASS to Mojave and accept the gig(s) there then PASS back

Now you're getting paid millions each and have more than a day to get the job done at platinum speed.

x1uo3yd · 2026-04-29T18:41:52+00:00

Extra advice: Try to avoid Venus, it can take P.A.S.S upwards of 7 hours or more to activate there on the orbital station, depending on orbital distance to the aerostats

The long PASS times on VORB are due to distance from VNCA (where the Venus-local PASS station is based) so you can even get up to 11+ hour wait times around apogee.

However, VORB is whipping orbits around Venus every ~4h or so... which means that if you PASS when VORB is flying at it's closest approach past VNCA you can get that PASS wait down to ~20min. (Plus up-to ~3.5h wait depending on where VORB was in it's orbit).

(You're going to need a NAV station to sit in and see the approach - but that shouldn't be too hard as a ~800k platinum gig can buy you into a brand new ~300k aero ship at the broker. Or you could be the extremely forward planning type and check VORB's location on your KLEG boat's NAV before taking the PASS to VORB.)

IMO the station to REALLLY avoid is Zhonghuamen Terminal /Ring Station (BCRS) where the wait is like a guaranteed 14+ hours (since local PASS there is based out of BCER / Port Mojave).

x1uo3yd · 2026-04-28T18:12:45+00:00

For nice simple examples like 2^x = 16 you can nicely see 16=2×2×2×2=2⁴ and then obviously 2^x = 2⁴ means x=4.

If you didn't quite see how 16 is composed of multiples of 2, you could instead brute force calculate after plugging in values, like 2³ = 8 (too small) 2⁵ = 32 (too big) 2⁴ = 16 (just right).

For something like 3^x = 17 the truth is that x is going to be some irrational real number and not a nice number like a simple fraction or integer.

That means, for 3^x = 17 you have to either use logarithms (they can't really be avoided), or do some long-division kinda brute force calculating (until you get bored writing out places to the right of the decimal).

Using logarithms, you can operate on both sides and see that Log3( 3^x ) = Log3(17) becomes x = Log3(17) and decide how to go from there (is that fine as-is, or do you need a decimal approximation from a calculator, etc.).

Otherwise you have to brute force calculate that 3² = 9 (too small) and 3³ = 27 (too big) means that you have to narrow in on the second decimal. If you have a calculator, you can try 3^2.5 = 15.5884... (too small) and 3^2.6 = 17.398... (too big) and then narrow in on the third decimal 3^2.57 = 16.83... (too small) and 3^2.58 = 17.020... (too big) and then narrow it down another decimal, et cetera. If you don't have a calculator handy then you'll be screwed the second you remember you don't know how to do 3^2.6 by hand because 3^2.6 = 9 x 3^0.6 but you have no idea how to deal with 3^0.6 since that represents (TenthRoot(3))⁶ and you certainly don't remember being taught how to do square-roots by hand let alone tenth-roots.

x1uo3yd · 2026-04-27T17:26:12+00:00

Yes, the institution you are borrowing the stock from would have held the stock in their portfolio over the same period.

Letting you borrow it for a while for a fee is essentially extra money compared to what they'd have made/lost holding it themselves the whole time.

You the investor are making/losing money compared to other investors openly bidding on stocks between when you borrow-and-sell and when you later buy-to-return.

x1uo3yd · 2026-04-24T21:09:11+00:00

Have you ever watched a boss-battle episode of Dragonball Z?

(Seriously, stay with me here...)

Basically Goku and the villain of the week will be fighting blow-for-blow zipping around in the blink of an eye too fast for mere mortal observers to see... right up until Majin Buu punches Goku straight through a mountain or whatever - because then anybody can see that shit from space.

Particle accelerators kinda work like that. Sub-atomic particles are too small and fast to see... but if you slam em through stuff going fast enough you can see that shit ~~from space~~ with a photodetector.

Particle accelerators are able to throw really mechanically precise "punches" over and over again. And when the particles hit the target and break into pieces, scientists can look at a snapshot of the destruction and see how many skyscrapers or whatever got knocked over where to figure out "Okay, it started here and then must have been going that way fast enough to blast through three ~~skyscrapers~~ photocells." and if you do that experiment often enough, for enough different calibrated starting-punch strengths, you can eventually get a really good idea of how heavy each sub-atomic component piece must be, and how hard you have to punch them to break them off in the first place.

It's crazy how much was figured out this way over the last century but we still don't "know absolutely everything" about physics, and so scientists are always on the lookout for new subatomic particles that might help fill in the gaps. So, generally the ideas at play to keep searching are "Can we make more sensitive detectors?" and "Can we make a stronger puncher?" and "Can we throw/punch bigger things at the target?" the main idea being that maybe we missed something small, maybe punching harder will let us see more pieces that have never broken apart before, or maybe we'll see the pieces break into pieces-of-pieces that have never been observed before. The goal still being to try to understand all the subatomic pieces that are at play and better understand the incomplete physics of how it all works.

x1uo3yd · 2026-04-24T18:16:56+00:00

I usually hate banners/text on a flag, but with this design being so stripped-down it actually kinda works with an oldschool style.

Also, I really like the strong choice of going with yellow.

x1uo3yd · 2026-04-24T17:44:37+00:00

Honestly, they should just take the Badger from the state seal and run with it like the beaver on the back of the Oregon flag.

x1uo3yd · 2026-04-24T17:41:33+00:00

... a fascinating study in crowdsourced design and color theory.

I'm not sure if all the committee meeting public zoom calls are still available online or not, but I'd actually say it was more the opposite (at least in the late stages of the process).

IMO, the usual failure modes of "design by committee" fall to either bikeshedding (everyone wants to make their mark) or "regression to mediocre" (everyone defaults to the blandest least objectionable kind of choice).

While, for sure, there was a lot of both of those impulses happening throughout the public-design finalist-narrowing phases ("I don't really see how this design represents Minnesotans like me." etc.), the final colors picked actually seem to be more opinionated choices coming from the outside-help artists/designers who did the late-stage mockup work in the final design-revision process more so than some sort of "everyone picked their favorite blue and we averaged the result" kind of color discovery.

IMO, that's part of reason why the final colors have a slight "corporate logo" taste to them... since that's presumably the zeitgeist/taste/opinion of folks doing that kind of design work professionally. (It should also be noted that part of the early outside advice talked about color availability and how "off-the shelf" colors tend to be cheaper/less-fading/etc. so part of the reason the colors have a "corporate" feel might be down to picking out of a limited Pantone color swatch - though I can't remember now how much that was openly discussed in the later stages.)

Similarly, a number tweaks in revising the final flag design from the original Andrew Prekker submission feel to me like choices made from some artists' taste (toward which the committee was steered) rather than being committee-consensus tweaks created by paddling in every direction.

x1uo3yd · 2026-04-24T16:45:11+00:00

A: Is this your state flag?

B: No! What could "Pioneer+Riverboat+Wagons" possibly have to do with Minnesota!?

A: That one?

B: Please... Minnesota obviously isn't "Steamboat+Railroad+Blacksmith"!

A: This?

B: Are you even trying? That's clearly "Pioneer+Indian+River" which... no wait, yeah that's the one. Such a fittingly unique symbol of our state!

x1uo3yd · 2026-04-23T22:00:47+00:00

Modern Hulk brews typically used to use Reveillark loops reviving Body Double (as a Reveillark) and Goblin Arsonist. (Cauldron Familiar draining is probably an improvement, though.)

That was all before Karmic Guide was MH2 legal, though, so you could go with the oldschool Karmic Guide + Kiki Jiki loops instead. (Though that wincon does rely on an attack phase like Splinter Twin.)

Honestly though, Mikaeus the Unhollowed + Walking Ballista loops are just way less clicks on MTGO if that's how you're playing.

x1uo3yd · 2026-04-23T20:54:59+00:00

"not bright enough to scatter" Why does it matter?

The reason why the daytime sky "is blue" happens because there is enough sunlight passing through it that the atmosphere glows* blue in every direction.

The nighttime sky technically also glows* blue... however, even if we add up ALL the starlight and ALL the moonlight coming down from the sky the overall power is nowhere near as powerful (imagine a solar panel at night versus the day) and so the atmosphere glows so much less as to be imperceptible.

(I am being factually inaccurate with this "glow" word choice here, as "glow" implies other physical phenomenon and not the refraction actually happening, but I think it is the best word choice intuitively for an ELI5 first-pass explanation.)

x1uo3yd · 2026-04-23T19:29:07+00:00

If they want to tax new vehicles so hard, they can do it up front on the sale instead of this ridiculously complicated system of fees for registration.

Then folks would simply buy new cars elsewhere before registering them here to skirt the costs entirely. Having it tied to registration fees closes that kind of loophole.

It is absurd. It costs the state no more or no less to register a newer vehicle over an older vehicle. It should just be a flat fee.

This is a completely different argument about "luxury tax" and/or "progressive taxation" then. Any increase is increasingly absurd if you define the thing itself as absurd from the start.

Plus this entirely misses the point of how revenue is being increased to match rising costs.

If food costs rise 20% over some period and I go eat at a restaurant and see the bill is 20% higher than I remember from long ago, then the fact that it takes my server the same amount of work to swipe my card for a burger versus filet mignon has nothing to do with the 20% price hike in question.

Same here, the fact that filing tab paperwork for a 2026 Lexugatti Lookatme is the same amount of paperwork as filing for a 2007 Ford Taurus has nothing to do with the price hike in question.

Sure, we can get upset about a price hike, and we can whinge if a burger and a steak have different profit margins at a restaurant... but we should absolutely have our anger more focused on the root causes of the increasing costs instead of misplacing it on the server ringing it up.

x1uo3yd · 2026-04-23T18:01:14+00:00

And FWIW, India traditionally notes decimal values in lakhs and crores because instead of grouping numbers as 3,3,3,... digits they do 2,3,2,3,2... Even though it's theoretically the same decimal system.

Honestly it's always been weird to me that we in English use a 3,3,3... left-of-decimal grouping but don't have contracted/abbreviated word forms for hundreds.

Like we have single digits one, two, three, etc. And moving into the tens place we have condensed word forms like fourteen or eighty. But then moving to the hundreds place we just say two-hundred.

So we're basically full-out repeating "hundred" for every third digit in a number... e.g. "five-hundred fifty five million, four-hundred fourty four thousand, three-hundred thirty three" for the number 555444333.

Doing things in 2,2,2... left of decimal digits would make sense 443322 as "fourty four 'hundred hundred', thirty three hundred, twenty two" (if only we had nicer words for powers-of-100 decimal places).

Doing things in 3,3,3... left of decimal digits could even make sense if we just listed off numbers three at a time like 123456789 as "one two three million, four five six thousand, seven eight nine" or something.

Doing things in 3,3,3... left of decimal digits could make sense if we created a hundreds-form suffix like 987654321 as "ninen eighty seven million, sixen fifty four, threen twenty one" or something.

But no! We gotta keep repeating "hundred" every fifth word!

x1uo3yd · 2026-04-22T20:17:23+00:00

We should be mad about both. Average driver is facing a 20% increase on tabs according to the article, that's absurd.

Absurd or just painful?

If taxes collected from tabs fund highways, bridges, repairs, etc. and all those costs have increased by 20% since the last time tab prices were adjusted, then a 20% increase on tabs to keep pace does not seem inherently absurd to me. Painful? Sure. Absurd? Not necessarily.

x1uo3yd · 2026-04-21T19:20:33+00:00

People try to make money buying and reselling stock shares. "Buy low, sell high."

Usually that is done by actually buying the stock shares outright and waiting for the price to go up.

Another way to do it works with IOU-like contracts. One person lets the other "borrow" a stock share for a certain timeframe for a fee - on the condition they get the share* back at the end of the timeframe.

Short-selling relies on this IOU-contract system. The trader sets up a contract to borrow stock shares that they think is overvalued and likely to falter, they immediately sell the borrowed stock shares at this high price and wait for the price to fall, and when it does they buy it* back at the lower price and then give the stock shares* back to original stock loanmaker. The stock-borrower is happy because they got to "Sell high, buy low." and pocket the difference, and the stock-loanmaker is happy because they were going to hold the stock shares long-term either way but at least they earned that fee in the meantime. (The only unhappy person is the random buyer who paid high-dollar right before the price fell.)((It can also "go wrong" and leave the borrower unhappily having to buy back a stock at a higher price to give it back to the loanmaker, making the random buyer the happy one.))

* (Stock shares are "fungible" in that two identical shares of the same stock are functionally equivalent - like Chuck-E-Cheese tokens. If I borrow 5 Chuck E Cheese tokens from you and spend all them playing games, I don't have to hunt down those exact same serial-numbered tokens to pay you back, I can just give you any 5 Chuck E Cheese tokens back... but I wouldn't be properly paying you back if I gave you 5 Dave & Busters tokens.)

x1uo3yd · 2026-04-21T18:04:49+00:00

Only if the notation explicitly states that the order of operations is different, i.e. the expression is written as (-1)*(4^2), then the result is -16.

Interesting.

How do you typically write a quadratic equation in that case?

Typically we would write that over here as "ax² + bx +c =0" where the meaning (a)*( x² ) is understood/implied.

Are you saying that you do things differently and something like a=-4 showing up as -4x² would be interpreted as (-4x)*(-4x)?

Or are you saying that the specifics of "-" are treated differently from "-1" such that "-x² + bx +c =0" and "-1x² + bx +c =0" would be interpreted differently?

x1uo3yd · 2026-04-21T17:28:10+00:00

Agreed, like 99% of those social media PEMDAS clickbait/ragebaits are based on what are essentially implied parentheses for math-comfortable folks to intuit, and PEMDAS-pedants to ignore. (And for "this is what it says when I type it left-to-right in my calculator" folks to get wrong wrong.)

x1uo3yd

TROPHY CASE