https://en.wikipedia.org/wiki/Rewriting

…if that’s too heady do note that if you have a heap of four marshmallows and a heap of five marshmallows then that’s the same as having a heap of five marshmallows and a heap of four marshmallows. To have a heap of nine marshmallows, though, you have to turn them into a single heap. That’s reducing the number of heaps from two to one and that’s a hand-wavy way to justify the term.

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 :)

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”.

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.

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.

My kitchen scales have a USB-C port. While I certainly would like it to have the capability to stream GB/s worth of measuring data over it fact of the matter is I paid like ten bucks for it, all it knows is how to charge the CR2032 cell inside. I also don’t expect it to support displayport alt mode, it has a seven-segment display I don’t really think it’s suitable as a computer monitor.

What’s true though is that it’d be nice to have proper labelling standards for cables. It should stand to reason that the cable that came with the scales doesn’t support high performance modes, heck it doesn’t even have data lines literally the only thing it’s capable of is low-power charging, nothing wrong with that but it’d be nice to be able to tell that it can only do that at a semi-quick glance when fishing for a cable in the spaghetti bin.

A and B are the original, used for host and device sides, respectively. C is the same on both ends of the cable because figures there’s device classes which can sensibly act as both, in particular phones. It’s also the most modern of the bunch supporting higher data transfer and power delivery rates because back in the days where A and B where designed people were thinking about connecting mice and keyboards, not 8k monitors or kWhs worth of lithium batteries.

The whole mini/micro shennanigans are alternative B types and quite deeply flawed, mechanically speaking.

Forks are derivative works (quite obviously) so yes you can forbid them via license terms. Whether or not that’s still open source, take it up with OSI. I vaguely recall that at least once upon a time there was some project that required modification to the code to be published as separate patches and it was generally accepted to be open source don’t ask me which.