That’s like asking a fusion researcher whether the reactor needs to reach 100 million Celsius or Kelvin, isn’t it.

Or signed integers because overflow is undefined. It could do the left-hand computation in two’s complement and the right hand in sign-magnitude, leading to different results. Or, as it’s undefined, it could brew you some coffee and serve it with an aspirin.

This is the flawed system, there is no method by which 0.999… can become 1 in here.

Of course there is a method. You might not have been taught in school but you should blame your teachers for that, and noone else. The rule is simple: If you have a nine as repeating decimal, replace it with a zero and increment the digit before that.

That’s it. That’s literally all there is to it.

My issue lies entirely with people who use algebraic or better logic to fight an elementary arithmetic issue.

It’s not any more of an arithmetic issue than 2/6 == 1/3: As I already said, you need an additional normalisation step. The fundamental issue is that rational numbers do not have unique representations in the systems we’re using.

And, in fact, normalisation in decimal representation is way easier, as the only case to worry about is indeed the repeating nine. All other representations are unique while in the fractional system, all numbers have infinitely many representations.

Instead of telling those people they’re wrong, focus on the flaws of the tools they’re using.

Maths teachers are constantly wrong about everything. Especially in the US which single-handedly gave us the abomination that is PEMDAS.

Instead of blaming mathematicians for talking axiomatically, you should blame teachers for not teaching axiomatic thinking, of teaching procedure instead of laws and why particular sets of laws make sense.

That method I described to get rid of the nines is not mathematical insight. It teaches you nothing. You’re not an ALU, you’re capable of so much more than that, capable of deeper understanding that rote rule application. Don’t sell yourself short.

EDIT: Bijective base-10 might be something you want to look at. Also, I was wrong, there’s way more non-unique representations: 0002 is the same as 2. Damn obvious, that’s why it’s so easy to overlook. Dunno whether it easily extends to fractions can’t be bothered to think right now.

The problem goes away easily once we understand the limits of the decimal system, but we need to state that the system is limited!

But the system is not limited: It has a representation for any rational number. Subjectively you may consider it inelegant, you may consider its use in some area inconvenient, but it is formally correct and complete.

I bet there’s systems where rational numbers have unique representations (never looked into it), and I also bet that they’re awkward AF to use in practice.

This is a workaround of the decimal flaw using algebraic logic.

The representation has to reflect algebraic logic, otherwise it would indeed be flawed. It’s the algebraic relationships that are primary to numbers, not the way in which you happen to put numbers onto paper.

And, honestly, if you can accept that 1/3 == 2/6, what’s so surprising about decimal notation having more than one valid representation for one and the same number? If we want our results to look “clean” with rational notation we have to normalise the fraction from 2/6 to 1/3, and if we want them to look “clean” with decimal notation we, well, have to normalise the notation, from 0.999… to 1. Exact same issue in a different system, and noone complains about.

By definition, all sufficiently advanced mathematics is isomorphic to witchcraft. (*vaguely gestures at numerology as proof*). Also Occam’s razor has never been robust against reductionism: If you are free to reduce “equal explanatory power” to arbitrary small tunnel vision every explanation becomes permissible, and taking, of those, the simplest one probably doesn’t match with the holistic view. Or, differently put: I think you need to look more broadly onto Occam’s razor :)

Avoiding other plants to take root, in particular ones with deep roots as they would form weak points in the dense felt-like root system grass has. Also ease of inspection.

There’s about a millennium of engineering experience in those dikes… and plenty of historical compromises. Like, we knew back in the middle ages that flat profiles secured by grass are the most stable and secure but they require massive amounts of material so it was necessary to use inferior dikes with vertical faces made of wood planks. Most recent notable innovation is sand cores and ditches behind the dike to manage seepage water (behind meaning on the land side, always confuses them tourists), and some minor alterations to geometry to improve the way waves hit it.

We probably knew that sheep were good for dikes before we built them as, at least in principle, dikes are nothing but a warft with a hole in the middle and we’ve built those since time immemorial.

And in case you’re wondering yes we’re raising them quite a bit higher in anticipation of sea levels rising. Completely uncontroversial decision, only question was whether to rise the dikes very high, or use the same budget to raise them not as high, but wider, so that they can easily be made even very higher in the future. We went with the latter option, which is kinda optimistic and pessimistic at the same time.

One night I dreamt about the new C standard. It was a tome of ten thousand pages, in dense, tiny, font, three columns of text on each page, and it was all headings and sub-headings interspersed with nothing but either “undefined” or “implementation-defined”.

Jutland in general. And really it’s less about the meat being good or bad, it is good, but we really rather have our sheep patrol the dikes and keep them healthy than eat them. Eating lamb while you’re wading in water leaves a nasty aftertaste.

Look, a stock photo!

Sheep are really as if made for that purpose: Unlike cows they cut the grass off clean instead of half ripping it out, and unlike horses their hooves don’t dig up the ground, but rather firm it up. Net result is healthy and short grass and thus a well-secured dike.

A massive population correction is inevitable.

The world population is going to stop growing, naturally, within the next decades as the last populous countries finish their demographic transition. It’s even going to see a reduction in many places unless steered against due to way below placement rate fertility. Long story short human fertility is intimately tied to child mortality: The fewer children die, the fewer kids we have, investing in quality over quantity.

The earth can easily sustain that population, even in a more fucked up state.

But is it a false premise? It certainly passes Occam’s razor: “They’re witches, they did it” is an eminently simple explanation.

Fun fact: C doesn’t even guarantee a + b == a + b

Furthermore, I’m not aware of any arguments worth taking seriously that don’t use logic, so I’m wondering why that’s a criticism of the notation.

If you hear someone shout at a mob “mathematics is witchcraft, therefore, get the pitchforks” I very much recommend taking that argument seriously no matter the logical veracity.

For a lorry, no. For a private vehicle, yes. Standard driving licenses only allow for up to 3.5t combined permissible weight (that is, vehicle and trailer plus maximum load), 750kg of those for trailer and load. If you want to drive a combination of vehicle and trailer individually up to 3.5t (so total 7t) you need a trailer license, anything above that you need a lorry license with all bells and whistles such as regular medical checkups.

Or, differently put: A standard VW Golf can pull almost thrice as much as most drivers are allowed to pull.

A small load for a private vehicle would be a small empty caravan, or a light trailer with some bikes. A Smart Fourtwo can pull 550kg which will definitely look silly but is otherwise perfectly reasonable, that’s enough for both applications.

Noone in the right state of mind uses decimals as a formalisation of numbers, or as a representation when doing arithmetic.

But the way I learned decimal division and multiplication in primary school actually supported periods. Spotting whether the thing will repeat forever can be done in finite time. Constant time, actually.

The deeper understanding of numbers where 0.999… = 1 is obvious needs a foundation of much more advanced math than just decimals

No. If you can accept that 1/3 is 0.333… then you can multiply both sides by three and accept that 1 is 0.99999… Primary school kids understand that. It’s a bit odd but a necessary consequence if you restrict your notation from supporting an arbitrary division to only divisions by ten. And that doesn’t make decimal notation worse than rational notation, or better, it makes it different, rational notation has its own issues like also not having unique forms (2/6 = 1/3) and comparisons (larger/smaller) not being obvious. Various arithmetic on them is also more complicated.

The real take-away is that depending on what you do, one is more convenient than the other. And that’s literally all that notation is judged by in maths: Is it convenient, or not.

yogurt with a sprinkle of random veggies

Don’t let Greeks or Turks hear that.

You need yoghurt, the heavy stuff with 10% fat, olive oil, garlic, cucumber, pepper, and salt. Nothing else. No, no dill, no mint (WTF?), no nothing.

Julienne the cucumber. Very fine is better than fine as long as you’re not producing mush. Salt it, let it stand for 10 minutes, then squeeze dry, toss the water. Add yoghurt, should be about two to three parts of yoghurt for one part cucumbers, by volume, don’t sweat it. Take about a clove for 500g of yoghurt (that’s a clove, not a bulb, yes it’s quite little, but it’s raw and it’s going to infuse), surgically remove the sprout (that’s where the nasty stuff is in garlic), chop finely. I said chop, not squeeze, yes it makes a difference. Add with pepper and salt and some olive oil, put in the fridge for at least one hour better a day, well covered (closed container is good, cling film if you have to), mix again and do final taste and consistency adjustment with pepper, salt and olive oil. Pepper should be subtle AF, supporting the garlic, not supplanting it.

…it’s absolutely fine to do other yoghurt sauces and in fact in Germany you’ll see three or four at any Döner shop, but don’t call the non-tsasiki tsatsiki, please. If you want a herb sauce, call it herb sauce. There’s no herbs in tsatsiki. (Sauces differ regionally in Germany – there’s always going to be tsatsiki, around here you also generally get curry, hot or mild, as well as cocktail sauce (no, not mayo based, it’s still yoghurt)).

Döner Kebab in bread is a much more recent invention than the same thing on a plate. Traditionally you’d get rice dunno how it’s in Turkey but in Germany there’s generally a choice of rice or fries.

Thus what you’re looking at is a Dönerteller mit Pommes, arguably a very sorry one. Technically the salad is present, in practice, no, salad generally consists of more than just onion. You can order “Nur Zwiebel” instead of “Mit Alles” but they’re going to feel sorry for you.

Decimals require you to check the end of the number to see if you can round up, but there never will be an end.

The character sequence “0.999…” is finite and you know you can round up because you’ve got those three dots at the end. I agree that decimals are a shit representation to formalise rational numbers in but it’s not like using them causes infinite loops. Unless you insist on writing them, that is. You can compute with infinities just fine as long as you keep them symbolic.

That only breaks down with the reals where equality is fundamentally incomputable. Equality of the rationals and approximate equality of reals is perfectly computable though, the latter meaning that you can get equality to arbitrary, but not actually infinite, precision. You can specify a number of digits you want, you can say “don’t take longer than ten seconds to compute”, any kind of bound. Once the precision goes down to plank lengths I think any reasonable engineer would build a bridge with it.

…sometimes I do think that all those formalists with all those fancy rules about fancy limits are actually way more confused about infinity than freshman CS students.

But sir… How did I create an extra room? You didn’t.

When Hilbert runs the hotel, sure, ok. Once he sells the whole thing to an ultrafinitist however you suddenly notice that there’s a factory there and all the rooms are on rails and infinity means “we have a method to construct arbitrarily more rooms”, but they don’t exist before a guest arrives to occupy them.

The only thing this proves is that the fraction-to-decimal conversion is inaccurate.

No number is getting converted, it’s the same number in both cases but written in a different representation. 4 is also the same number as IV, no conversion going on it’s still the natural number elsewhere written S(S(S(S(Z)))). Also decimal representation isn’t inaccurate, it just happens to have multiple valid representations for the same number.

A number which is not 1 is not equal to 1.

Good then that 0.999… and 1 are not numbers, but representations.

Without computation there’s neither which is why CS always wins.