FishFace

Drive to each others places and don’t drink. You don’t need alcohol to have a good time with friends. Hang out online. Meet people who live in walking distance.

None of these options is perfect; we’d rather be able to meet exactly whom we want, and do exactly what we want when together. But the topic is socialising, not socialising in exactly the way we prefer.

Most of my friends don’t live in the same city as me, so it’s not easy for me either. But by one method and another I still have social contact.

As an external observer to this conversation, you’re not reading taking part in good faith. Try to understand the intention of their replies.

It depends wildly on the fruit and vegetable. For example, cabbage is about 0.25 calories per gram but carrot is 0.36, and strawberries are 0.32. An apple is 0.5. (All numbers from Wolfram Alpha).

When you set up arithmetic from absolute first principles you typically say that there is an operation called addition, an operation called multiplication, that they are related by the distributive law, and then you assert that there are identities for these operations, which do nothing: adding zero does nothing, and multiplying by one does nothing, so zero and one are the additive and multiplicative identities.

Next you add that each element has an inverse under these operations. The additive inverse of a number is its negative, so the inverse of 2 is -2. The multiplicative inverse of a number is its reciprocal. The defining feature is that the inverses cancel the operation leaving just the identity, so 2 + -2 = 0, and 3 × 1/3 = 1. The exception is that 0 does not have a multiplicative inverse.

With this, the operation of subtraction is defined in terms of addition and additive inverse, and division is defined in terms of multiplication and multiplicative inverse.

Saying that one is “syntactic sugar” for the other is standard in higher mathematics, but of course you could go through the same procedure starting with subtraction and division, and defining inverses in terms of those operations - the result is no different. The reason starting with inverses is preferred though is because there are lots of structures which have an operation and an identity for it, in which you can ask the question “are there inverses” because inverses are defined purely in terms of an operation and its identity. You can’t ask the question “can you divide in this structure” if the only way to even have a concept of division is to start with one.

This topic is the beginnings of abstract algebra which starts with group theory and builds from there.

I think of you looked hard you’d find it :) And it’s even easier to find / used to indicate division which has all the same issues.

Chrome market share seems to be fairly steady over the past year…

Well, you sure did repeat your assertion!

But it’s not so great for polynomials and other more complicated expressions which you’re not just evaluating, but rather manipulating algebraically:

3 y × 3 ^ 4 y × 2 ^ + -2 y × + 3 +

I’m talking about exercises in textbooks, and you can find enough examples that writing them off as “the exercise is bad” is not really a good enough response.

The only way the exercise is bad is if it causes confusion in the people who are using the textbook. Those students have been exposed to the conventions of the textbook in question; they’re not people who were brought up on some other convention. You do see inline division and the vast majority of people interpret an expression like that above the way I said, so it’s not in practice confusing.

It’s not realistic to demand that every textbook uses the same conventions. It is realistic to demand that they lay out such conventions explicitly, which they unfortunately don’t.

Not sure where that comes in…

This is not true. It typically falls out of use in high school and rarely shows up after, but it’s not like it’s banned or anything like that.

Depending on circumstance, I don’t like to block without saying the criticism behind it. If I’m then going to block, I prefer to announce to make it clear to the blockee that I won’t be replying, and to make it clear to everyone else why I haven’t replied, if the blockee chooses to reply. Works for me.

It’s not unheard of to find, in an exercise, “Simplify 4x²/2x”. The answer is almost guaranteed to be 2x. (There are some interesting exceptions, but they’re not really important). More often such a question would use fraction notation, but not always, to prevent exercises taking up too much space.

What’s going on is that the multiplication of the 2 and x, because they are written without a symbol in between, is seen as morally being something you should do first.

And in such exercise contexts, it’s unlikely to be misunderstood. But it’d still be better to be clear about it.

It’s also because writing multiplication without a symbol creates a tightly bound visual unit that is typically evaluated before other things. If you see an exercise like, “what is 4x²/2x” most people answer “2x” not “2x³”. But this convention is rarely taught explicitly, so it’s ripe for engagement bait.

Uh oh, here we go! Before the Fediverse’s favourite mathematical charlatan comes to play, let’s lay out a few facts:

• This is an unusual way of writing down this expression: you would not normally mix in-line division (written with ÷) and multiplication written without a symbol. It’s written this way on social media to for engagement bait.
• Because of this, a perfectly valid reply is to ask “can you put in some brackets to make it clear” :)
• A strict, standard reading of the order-of-operations as abbreviated by PEMDAS, BODMAS, etc, is to perform multiplication and division in the order that they occur. This would mean the evaluation goes like this:
  1. 6÷2(1+2)
  2. Perform addition inside the brackets: 6÷2(3)
  3. Perform the first multiplication or division: 3(3)
  4. Perform the remaining multiplication: 9
• Occasionally, PEMDAS is interpreted as indicating that multiplication must be done first because the M occurs before the D. This is not usually how it is taught, but rarely it happens. This would give you 1 but, to be clear, in most places this is wrong. I myself was taught BODMAS and, in fact, do division first in all circumstances.
• Much more commonly, though, the actual practical order in which mathematicians, teachers and students all evaluate expressions is a little different, in that it evaluates symbol-less multiplication (also known as “juxtaposition” which just means “writing two things next to each other” or, in discussions about this topic in particular, “implicit multiplication”) before anything else. This is done because writing two things next to each other creates a tightly-bound visual unit.

It’s rare for this last point to be mentioned explicitly as a violation of the order-of-operations. It usually only becomes relevant well after those conventions are spelled out (which is typically done in late primary school or early high school) after children start learning algebra and how to write algebraic expressions: using letters to represent unknown quantities, omitting the × symbol. Exam boards and textbooks are usually quite careful to avoid writing problems in which this unstated rule actually matters.

It’s important to realise that the order in which we evaluate a mathematical expression is a matter of convention. After establishing how to add, multiply, subtract or divide two numbers, it is a separate question which operations should happen first when more than one is written together. This is why we need to teach students the order of operations - they can’t just work it out themselves. Having said that, it certainly makes a lot more sense to do multiplication before addition, and exponentiation before multiplication, because each of these operations is (typically: you can define them in different ways if you’re a masochist) defined in terms of the previous one. This means that if you have an expression involving all three, and you first turn all the exponentiation into multiplications, you are left with a simpler expression that means the same thing. This only happens if evaluating exponentiation is the first thing you’re supposed to do. However, it would be a mistake to think this means that there is any mathematical necessity about this: what a sequence of squiggles on paper means is entirely up to the people reading and writing the squiggles; as long as they agree, the person reading the squiggles will get the same answer as intended by the person writing them. There’s a good, lengthy write-up here

This means that while what I was taught is “wrong” according to how it is usually taught (including today in the same country), this wrongness is better understood mathematically as “unusual” - something that needs to be worked out by communication and consensus rather than by dictating one right and another wrong.

You do get some people with very strong opinions about this, which is not always correlated with their actual knowledge. If the aforementioned charlatan turns up, I’ll explain…

This isn’t a shitpost and you sound like you need to calm down and touch grass. To aid my own touching of grass, you’re going on my blocklist.

I don’t understand why this is a shitpost

I didn’t signal to change lanes until BMW made a car even more obnoxious than I am

Weird flex, but OK

That sounds like a bad way to ensure the survival of your offspring?

Early cars were worse than trains and horses. It took a lot of effort to make them useful, and then to make them ubiquitous.