#mathsmonday — Public Fediverse posts

#MathsMonday #Mathematics
1/7
Oliver Knill (iii)
This week back to Knill's blog post...

"There are two interpretations" - one of which violates the rules of #Maths and is thus unambiguously wrong

"It is not clear what the textbook had intended with the 3y" - says someone who clearly didn't look in ANY textbooks 🙄

"Yes, one could argue that without brackets the given order matters" - no, you can't. Order NEVER matters in #Math, but obeying Left Associativity does! https://dotnet.social/@SmartmanApps/110965810374299599 ...

1/8
#MathsMonday #Maths #Math
Oliver Knill (ii)

"2 page paper with source texts appendix" - None of which were #Mathematics textbooks, and still wrongly citing Cajori

"We often write x/yz meaning x/(yz)" - We ALWAYS mean that 🙄

"That brackets are required to avoid any confusion was noticed in (Lennes)" - Not only did Lennes NOT say that, quite the contrary he repeatedly pointed out there was only ONE possible answer, a÷bc=a÷(bxc) and a÷bxc does NOT equal a÷(bxc) https://dotnet.social/@SmartmanApps/117069305759444296...

1/9
#MathsMonday
#Mathematics #Maths #Math
I want to come back to Lennes' letter, which I've covered previously at https://dotnet.social/@SmartmanApps/110965810374299599 but that time it was because I had seen it referred to as being evidence for a "new rule" (it wasn't), whereas this time Oliver Knill https://dotnet.social/@SmartmanApps/116990848347700650, who I'll come back to next week, is claiming it's evidence of "ambiguity" - not only is it not evidence of that, it's evidence of the complete opposite! So this time round...

1/6
#MathsMonday
I ran a #Mathematics #Maths #Math #poll this week about 18÷3x2 https://dotnet.social/@SmartmanApps/117006976986454267 and the votes have stopped rolling in now, so time for the big reveal...

TL;DR

BEDMAS/left-to-right 18÷3x2=6x2=12

and crucially...

PEMDAS 18÷3x2=18x2÷3=36÷3=12
and NOT 18÷(3x2)=18÷6=3

Those making that mistake were 16% of the vote, thus debunking the claim that "most humans" would get an answer of 3 - 84% got the correct answer of 12, including some who were correctly following PEMDAS...

1/6
#MathsMonday
This week I'm kicking off a new #HallOfShame series, about spreaders of #disinformation #misinformation about #Mathematics, or as I call them, the #disinformati. Some have #Maths qualifications, some only have Physics(!) qualifications, and some don't have any qualifications! I do usually try to avoid shaming people, but I got fed up with people repeatedly using these wrong references(!), so I'm going to link their claims to the #Math disproof of them...

1/x
#MathsMonday
I'm coming back to #Mathematics order of operations (hopefully) one last time, just to flesh it out with some more #Maths textbook references, for those who want it (having only initially given one in each case). Not going overboard, just 4 #Math textbook screenshots per post (since Mastodon only allows 4 pics per post, that's a good number to finish it off with). I may come back in future, if some particularly good ones come along, hence unknown post count for now...

1/7
#MathsMonday #Math
I've seen multiple #Maths people quote page 274 of Florian Cajori's history of #Mathematics notation, which is available at https://archive.org/details/historyofmathema031756mbp, and yet they always fail to read not only anything else from the book, but not even the rest of the very section they are quoting from about division! This is a classic example of something I have talked about previously, at...

1/10
#MathsMonday
This article was referred to me - https://puzzlewocky.com/brain-teasers/probability-puzzles/every-shuffle-of-a-deck-of-cards-is-probably-unique-in-history/ - and it's a classic case of #Mathematics #disinformation being spread by someone who clearly has no #Math qualifications (well, certainly not Statistics anyway), so here's the ACTUAL #Maths involved...

"Dividing our estimate of the number of shuffles in history by the number of different ways a deck of cards can be ordered gives our odds that" a PARTICULAR order will occur, such as all the cards in value order...

@tknarr @SmartmanApps @WahFo I highly recommend reading a few of this guy's #MathsMonday pinned threads to get an idea of the extent of his mathematical understanding, and the chances you have of convincing him of anything. The ones about 0.999... are particularly illuminating.

1/3
#MathsMonday
This week I was planning a future #Mathematics thread, and had cause to refer to the 5 rules of #Maths which make 8/2(1+3) equal to 1, and nothing else (the only way to get anything else is to break one or more of these #Math rules! Which of course you're not allowed to do), and, as is not unusual, after the first 4 I remembered I then had trouble remembering the 5th - usually a different 5th one each time(!) - so I decided to tie them all up in a neat thread this week...

1/5
#MathsMonday
I'm coming back to a point I've covered before, but this time adding #Mathematics textbooks for the sake of completeness, that being the history of what Division meant in #Maths, with emphasis on what it means now in #Math

Up until at least the 17th Century everything that followed a division symbol was in the Divisor. We can see that in Teutsche Algebra (1659), on page 76, where 7÷GG+1 means 7÷(GG+1)....

1/4
#MathsMonday #Mathematics #Math
This week a note about the rules of #Maths, but first, the picture...

I saw Mules get mentioned this week, and had a funny thought, "Mules works as an abbreviation of Mathematical Rules", which then lends itself to saying some funny things like, "the Mules say to multiply first", or the sign in this pic could be read as "Mule multiplying". 😂 I look forward to this being word of the year next year 😂

Anyhows, the main point this week relates to the Mules...

1/5
#MathsMonday #Maths #Math
This week a commonly-forgotten rule of #Mathematics - because we usually skip these lines of working out and go straight to the solution - when we substitute a value for a pronumeral, the value goes in brackets. i.e. if a=3, then 2a=2(3), not 23, because 2a=6, not 23. We can see this explicitly demonstrated on page 36 of Modern Algebra https://archive.org/details/modernalgebrastr01dolc_2. If showing full working out (which Modern Algebra skips) then the next step is to apply...

@citc
"In case unaware, we are in a "post-truth"/"my truth" nonsensical world of "the alternative fact(s)" - welcome to my #FactFriday and #MathsMonday series to correct that, as well as the odd observation here and there on other matters, as above

"Then they scroll on" - well, speak for yourself. I still have the odd thing here and there that I posted months or years ago getting liked/boosted again by people discovering it for the first time. Turns out people like facts and truth-tellers

1/3
#MathsMonday #Math
I've seen 2 people in #Mathematics claim recently that we can't prove that a+b=b+a - the Commutative Property - and that we just accept it as true. Nope, not only is it literally proven, but we show students the proof when we teach this to them. File this under "Mathematicians forget what they were taught in high school, again" (along with The Distributive Law, which I just happened to be teaching to my Year 7's last week). There are multiple #Maths proofs of this...

( I still don't get the right-angled triangle sides' worked solution in the appendix though.
I literally did a physics degree, somehow.
The step up to (x^2 - 1) > 2n or whatever is fine.
Right after that looks like (x^2 + 1) - (x^2 - 1) > 2 from nowhere.
Like wtf?
Did I just have a stroke.
Where the hell did that come from and go, fucker-eyed crow?)

#math #maths #MathsMonday #MathMonday #mathematics #ALevelMathematics #STEM #book #books #Books2026 #Read #Reading #ReadingList #ToRead #FreedomToRead #story #stories #literature #kid #kids #Child #Children #ChildrensMentalHealth #ChildrensLiterature #Teen #Teens #Teenagers #autistic #AutisticJoy #Autism #AutismAwareness #AutismSpectrumDisorder #AutismSpectrumCondition #Asperger

Here we are again on #MathsMonday, looking at the questionable statements of SmartmanApps, #debunking the #disinformation and seeing what real #mathematics it accidentally uncovers.

Our now-familiar friend says that infinitesimals are a standard thing taught in schools. This is false, with the possible exception of wherever he teaches, because infinitesimals have by and large been ejected from mathematics due to being unnecessary and confusing.

But what is true is that infinitesimals *used* to be taught, and he has the very old textbooks to prove it. Let’s find one of those textbooks, and its definition of infinitesimal:

> lim a = 0 means that a is an infinitesimal quantity

(Advanced Algebra, p226 by Collins, J. 1911. American Book Company. Symbols altered for typographical necessity)

So we need to know what “lim x = a” means, which is furnished to us on page 297 (it is no credit to this textbook that it uses undefined terms without even an apology):

> If a variable x assumes a given sequence of values such that the numerical difference between a constant a, and the variable x becomes and remains less than any assignable quantity, however small, then x is said to approach a as its limit [written] lim x = a

This is essentially the way Cauchy defined limits, and is the same as the definition of a limit I gave last time, with two changes:

1. It’s less easily translated into the symbolic version due to not using directly equivalent language like “for every”.
2. Instead of a sequence, we talk of a “variable”.

It is the second difference which is more consequential. In modern mathematics, in any given context, a variable only takes on a single value. If you think of x as possibly taking on multiple values, say 2 and 0 in alternation, then the following argument no longer works:

“x is not less than 1, and x is not greater than 1, therefore x is equal to 1”.

Imagine asking “is x less than 1?” and finding that x could be 2, so answering, “no”; then we may ask “is x greater than 1?” and find that x could be 0, so answer “no” again. But concluding that x is equal to 1 is not valid. So, we must be smarter about such arguments. Maybe our Smart friend is that smart, but I would prefer not to depend on it.

The solution modern mathematics has taken to this is that if we want to consider a changing quantity, we encode it into a different kind of object: a function. The function accepts a parameter, and that parameter determines what value it returns. Thus the dependence of that value on the parameter is made explicit; we save ourselves from the possibility of getting confused, because “x(0) is not less than 1, and x(1) is not greater than 1, therefore x(2) is equal to 1” is obviously rubbish!

In school it is typical still to describe functions in the old-fashioned language of variables, so you probably remember seeing a linear function described by “y = mx + c”, where x is a variable, and y another variable which *depends* on it. Further on in school it’s typical to replace “y” with “f(x)” which makes this dependence explicit.

Because functions are an entirely different type of thing, we also never compare them to numbers without first describing exactly how that comparison should happen. We don’t ask, “is f equal to 1”? Because the answer is clearly “no”, and similarly f is not less than or greater than 1; f is a function, not a number so these questions don’t even really make sense. This is not the case with variables; it is perfectly reasonable to ask whether x is equal to 1 - this kind of question is embedded in every single equation a school pupil is asked to solve.

Clearly, mathematicians and pupils of yesteryear were all able to work like this, but it is unnecessarily confusing and error-prone.

## Sequences

So, we will use functions instead of variables, and since it will not cause any extra difficulties, we will specifically use sequences which are functions whose inputs are natural numbers. This turns Cauchy’s definition of the limit into the modern one, and it turns his definition of an infinitesimal into “a sequence with a limit of zero”.

We have some questions to answer: while it is natural to compare a variable to numbers (such as when solving a system of inequalities) comparing a function (or sequence) to a number is less natural. What does “sin < ½” mean? Is it true, or false? Clearly sin(x) < ½ for some x but not for others.

Nonetheless, if we want sequences to occupy the role of infinitesimals, we need to be able to perform such comparisons, because the fundamental property of an infinitesimal e is that 0 < e < 1/n for all natural numbers n. Thus how we set up infinitesimals is fundamentally a matter of how we set up rules for comparing the sequences which represent them.

Let us first point out that instead of comparing sequences to *numbers* we can replace any fixed number with the constant sequence all of whose elements are that fixed number. And secondly, let’s establish that the *normal* equality of sequences is simply that each of their corresponding elements must be equal, that is, their first elements must be equal to each other, their second elements must be equal to each other, and so on. This means that there are many sequences whose limit is zero but which are not equal to one another. One of those sequences is the constant sequence all of whose elements are zero, i.e. the sequence which we are using instead of the number zero, written (0, 0, 0, …)

I should point out here that it is a standard fact about limits that the limit of a constant sequence is always that constant. This should be easy to see from the definition, but in a university course you would prove it rigorously. This means, also, that any sequence whose limit is zero must be different from any constant sequence, except that the zero sequence is equal to itself. This is good for our use of sequences which converge to zero (i.e. have limit zero) as infinitesimals, since they should be different from numbers larger than zero.

## Equivalence and Order

But we still have to do more work, because to be infinitesimals, these sequences need to be smaller than 1/n, for every natural number n. We know the first step to making sense of this: replacing 1/n with the sequence (1/n, 1/n, 1/n, …). The next step is creating a notion of “smaller” and “larger” sequences.

In what follows, I will fix a sequence e representing an infinitesimal, e := (1, ½, ⅓, ¼, …), and x representing a small finite positive number, x:= (0.1, 0.1, 0.1, …)

### Global Domination

One very simple way of setting up an ordering is to say that (a1, a2, a3, …) < (b1, b2, b3, …) if a1 < b1 and a2 < b2 and a3 < b3, and so on, for each index. This is no good for our purpose, because look at e and x. If we are doing things right, we should have e < x, but e1 = 1 is not less than x1 = 0.1. Even worse, if we go to the 11th element, x11 = 0.1 is not less than e11 = 1/11, so neither e < x nor x < e: this is not a **total** ordering, i.e. sometimes two objects just do not lie in any particular order.

### Lexicographic Ordering

The lexicographic (so called because it’s the ordering used by dictionaries - i.e. lexicons) ordering is perhaps the next most obvious way of ordering something that’s made out of multiple things which are themselves ordered.

Using this ordering we’d say that (a1, a2, a3, …) < (b1, b2, b3, …) if a1 < b1, or a1 = b1 and a2 < b2, or a1 = b1 and a2 = b2 and a3 < b3, or … and so on.

This *does* give us a total order; we can compare any two sequences and either one is less than the other, or they are exactly the same sequence. However, we still have a problem because we find that since 0.1 < 1, we have defined x < e, which is not what we wanted.

This ordering fails to capture the idea that it is the *eventual* behaviour of infinitesimals that we care about, and instead makes the early behaviour the most important.

### Eventual Domination

We can’t just do a “reverse lexicographic order” because we can’t start at the *last* element of a sequence composed of infinitely many elements.[^4] But we can do something else: we can say that (a1, a2, a3, …) ≤ (b1, b2, b3, …) if *from some point* all the a’s are smaller than all the b’s. You can hopefully see that, with this ordering, e ≤ x: from the 11th element onwards, all e’s are below 0.1. And indeed if y is *any* constant sequence consisting of rational numbers, eventually e will drop below that number and stay below.

It is not for no reason that I used ≤ in this definition instead of <. That is because this is again not a total order among all possible sequences: a sequence could oscillate above and below another sequence forever.

### Ordinary Real Numbers

What Cantor did in his development of real analysis was to notice that there is a certain kind of sequence that behaves very nicely, which nowadays we call a *Cauchy sequence*. It has the property that as the sequence continues, its values become arbitrarily close to all later values:

> A sequence a is *Cauchy* if, for every ε > 0, there is a number N such that for all n, m both greater than N, |a(n) - a(m)| < ε

The structure Cantor worked with was all of *these* sequences (of rational numbers) rather than arbitrary sequences. Then, he said that two sequences were equivalent if the difference between them becomes arbitrarily small. If not, then (one can prove) the difference between the values of a and b is either eventually positive, in which case we say a is larger, or eventually negative and we say b is larger.

We can go on to define arithmetic between such sequences and prove that everything works out wonderfully but there is one snag for us: there are *no* infinitesimals! What was the fate of our supposedly infinitesimal sequence e? Well, unfortunately the difference between it and the zero sequences becomes arbitrarily small, so they are rendered equivalent: any sequence which is “infinitesimal” in the Cauchy sense becomes merely zero.

[^4]: Unless the infinite order type is a *successor ordinal* which is a concept beyond the scope of this post, and is not the case for our sequences.

#math #maths

1/2

It's so funny this popped up in my feed today https://bird.makeup/users/julia_doubleday/statuses/2057947414334492782 because I'd already decided my next #MathsMonday (hopefully this week, if I have time) is about a PhD student who didn't read the textbooks they cited in their thesis! 😂

1/5
#MathsMonday
This week I will debunk several false claims made about brackets in #Mathematics on socials - there are several! Actually it's easy to just check for yourself, at https://dn790009.ca.archive.org/0/items/historyofmathema031756mbp/historyofmathema031756mbp.pdf but I'm gonna save you some scrolling. 🙂 Firstly you can see in the screenshot that arithmetic has been around in #Maths since at least Egyptian times, and that we have had the modern + and - in #Math since the 16th Century...

1/6
#MathsMonday
This week #scaffolding, as used in #Mathematics (and other) #textbooks, as I'll be referring to this in two upcoming #Maths threads. The name is taken from the scaffolding used when buildings are being erected, and removed when construction is complete. In #Math textbooks (and worksheets) this takes the form of hints/tips at the start of a chapter/exercise, to help the student understand the process, and no longer appear once the student has thus learnt how to do it un-aided...

Time for another round of examining the interesting beliefs of SmartmanApps and #debunking the #disinformation this #MathsMonday.

We saw last time that his view of mathematics is at odds with that of the mainstream: I enumerated the standard axioms of the real numbers and proved that there can be no number 0.999… that is simultaneously less than 1 and greater than 0.9, 0.99, and any such finite decimal truncation of 0.999….

His idea is that 1 is “the limit of” 0.999…, but not the exact value of it. But what exactly is a limit? Let’s have a look at what our Smart Friend calls a limit:

> The limit is the number which [the sequence] never reaches

(see https://dotnet.social/@SmartmanApps/116303201093245275 I am not quite certain he intends this language to apply to all sequences, but I have not seen other descriptions from him)

This is simply inadequate, and it’s worth seeing why such poor explanations are inadequate with some examples.

* The sequence (1, 1, 1, …) *never reaches* the number 2, so is 2 the limit? The same applies for every number greater than 1, so are all of them the limit? The wording “the number” implies that the limit should be unique.
* On the other hand, it *does* reach 1, which intuition says ought to be the limit of this sequence.
* The sequence (1, 2, 3, 4, …) will exceed every number eventually and so, I guess, “reaches” every number. Again the wording “the number” suggests that such a number always exists, but apparently does not.

It may be that the Genius has a more precise idea of limit lurking in his mind, but to tease it out we’d have to interrogate him about these (and probably other) examples, and most likely anyone who tried would get blocked before they could complete their investigation.

The usual definition can be seen clearly from the early 19th century, due to Bolzano, though its roots go back further. That definition is:

> For a sequence (a_0, a_1, a_2, …), and a real number A, if for every real number ε > 0, there is some natural number N such that for every n > N, |a_n - A| < ε, then we say that A is the limit of the sequence (a_0, a_1, a_2, …).

This is quite a mouthful, and first year mathematics undergraduates spend quite some time getting the hang of it. A characteristic of the definition is the alternating *quantifiers*, which are written out “for every” and “there is” here (but would normally be written with symbols). It took mathematicians some time to come up with this modern version of quantified mathematical language.

Nevertheless we can put it into simpler language, at the cost of a little precision: **the limit of a sequence is A if the sequence gets as close to A as we like and remains that close forever**. It’s important that we keep that “remains that close” in. It’s important that neither of these ways of describing the concept assume a limit exists, because not all sequences have a limit. It is quite easy to prove directly from the definition and the properties of the real numbers that:

* A constant sequence (a, a, a, …) has a as its limit
* If a sequence has a limit, the limit is unique
* The sequence (1, 2, 3, …) does not have a limit

The ordinary way of proving such basic facts is via our friends Completeness and the Archimedean property. Our pal has explicitly rejected these (by affirming the existence of infinitesimals) and so does not have them available for this purpose.

To see this practically, how should we prove that the limit of the sequence (0.9, 0.99, 0.999, …) is 1? The ordinary way would be to appeal to the definition:

1. Pick any positive distance ε. By the Archimedean property, ε > 1/N > 1/10^N for some N
2. If n > N then 1-0.99…99 (with n nines) is less than 1/10^N < ε, so 1 is the limit.

The astute reader will notice this argument is very similar to the one from last week. But if infinitesimals exist, we *cannot do this*: the first step is, in fact, false. If ε is infinitesimal, then there will not be any N such that ε > 1/N! That is in fact what it means to be infinitesimal!

Specifically, if ε = 1 - 0.999…, which the Smart Man says is greater than zero, this argument falls down; we cannot get the sequence (0.9, 0.99, 0.999, …) to be ε-close to 1 if ε is infinitesimal by looking to some point far enough into the sequence: for any n, the nth term 1/10^n away from 1, and 1/10^n is larger than ε.

From further reading of SmartmanApps’ posts, I suspect he might want to object that if we continue the sequence “to infinity” the difference becomes infinitesimal. I should be very clear here: sequences as here defined and as used by him cannot be continued “to infinity”. The defining rule for this sequence is that the nth term is 1 - 1/10^n, something which makes sense and is defined for *natural numbers* n, and because infinity is not a natural number and 10^∞ is not defined, we can’t just continue like that. The only way would be to make a *definition* of what 1 - 1/10^∞ means, i.e. to *choose* what happens at this continuation; there are no axioms governing rational numbers that force us to give a certain value to this expression.

Another potential objection is that I have used the “wrong” definition of a limit, but:

1. You can find this definition in every single textbook and set of lecture notes on real analysis
2. You can find this definition (written in an old fashioned way of "variables that take on successive values" rather than sequences) in the 120-year old algebra textbooks he loves to cite
3. We saw multiple problems with his broken pseudo-definition that make it useless

so it’s up to him to provide a correct one. One could try as a first attempt to replace “for every real number greater than zero” with “for every non-infinitesimal real number greater than zero”. But without Completeness, basic facts like the uniqueness of limits, on which many more important theorems rest, would still be false.

It’s fun to explore what happens to mathematics if throw out some of its founding principles, though it does make doing anything useful with it hard. Forget working out anything truly useful like calculus without Completeness, or something precise to replace it!

Next time I plan to look a bit more at infinitesimals and how you can treat them rigorously.

#maths #math #mathematics

# Introduction

Right, it's time to start the big #debunk! This is a story of #mathematics, #education and one Smart Man. It is a debunking of the arrogant proclamations of SmartmanApps (a maths teacher who lacks both knowledge and pedagogical skill) as well as a lesson in the limitations of education, and hopefully along the way I’ll highlight some interesting areas of mathematics that are not illuminated by a high school #maths education, but which nevertheless are quite accessible. The intended level is that of a curious high-school student. I will attempt only to give the necessary details, so if you are left feeling like you need a reference, or more information, let me know and I’ll gladly point you in the right direction.

I acknowledge the audience for this will be small, but it nevertheless needs to be done. (It's certainly unlikely that the user in question will read it, as despite at first having an apparently limitless capacity to reply with new claims, and raining scorn on those who gave up replying or blocked him for their own sanity, he nowadays seems to block anyone who engages with him for more than a handful of posts - including me).

The first topic (in the thread below to avoid clogging your feed) will simply be the real numbers, and how the number 0.999… illuminates the mathematics of them.

Oh, and since it's fitting... #MathsMonday :)

1/9
#MathsMonday #Mathematics
This rubbish article https://www.scientificamerican.com/article/mathematicians-cant-agree-on-whether-0-999-equals-1/ popped up in my feed a few times, and I've already debunked the various points, but will cover it with specific links for each (non-)point.

"Mathematicians can’t agree on whether 0.999... equals 1" - yes they can, it's not, as per division, limits, infinite decimals, and other #Maths topics, all found in #Math textbooks

"by Manon Bischoff" - "is a theoretical Physicist". Maybe just stay in your lane dude... 🙄

@binford2k @TechDesk @404mediaco @emanuelmaiberg
"nobody asked you whether one out of 65,380,334 pages was correct or not" - and I never said anything about one page, but MANY pages 🙄

"That’s 0.000001529511917% of Wikipedia" - that's a strawman

"You have a hell of a long way to go before you’ve supported your “full of misinformation” claim" - go ahead and search for #MathsMonday to find a whole bunch more (and that's only for Maths)!

1/5
#MathsMonday #Mathematics #Math
This week I'm coming back to the topic of 0.(3) only being approximately equal to 1/3, which I discussed previously at https://dotnet.social/@SmartmanApps/115207065189190900

At the time, I knew this was true simply from knowing doing the division always leaves a remainder of 1. Since then I've now seen 2 #Maths textbooks which explicitly spell this out, that all non-terminating decimals are only approximations, and that only terminating decimals are exactly equal to fractions...

1/6
Further extending this #MathsMonday on the laughable Cantor #Mathematics claim that the "infinite sets" of the Naturals and the Evens are "the same size", let's accept that #Math argument for a moment, and prove by contradiction that it can't be true...

If sets can be infinite, that means not only do they come with the #Maths bracket form of set notation, and cardinality, but also set operations, like Union and Intersection, and ways to depict those sets/operations... with Venn diagrams...

1/9
Coming back this #MathsMonday to Cantor (who has regrettably been filling my #Mathematics timeline again), we have https://www.quantamagazine.org/how-can-infinity-come-in-many-sizes-20260223/ which lays out his (non-)proof in layman's terms, so let's look at the specifics of the #Maths...

"Aristotle rejected the existence of the infinite entirely; to him, infinity was simply a limit that could never be reached, not a true mathematical entity" - yep, and this is what is still taught about #Math limits and infinity today...

@everton137
Yes, me. Not every week, but most weeks, I write a mini-thread about Maths - #MathsMonday - because I've seen enough #disinformation #misinformation on #Wikipedia to know the only true way to spread the word is to have a place where no-one else can back out your literal textbook quotes (notably the Wiki Maths pages in question never cite any actual textbooks 🙄 ). Here's an index thread of everything I have posted so far... https://dotnet.social/@SmartmanApps/110968910722113903

1/x
#MathsMonday #Maths #Math
Over time I've saved many screenshots of #AI #slop #aiSlop stuffing up #Mathematics big time, and on occasion I've had cause to reshare them, and at times I have cursed that I can only attach 4 pics per post. Then I realised, what am I worried about - just post them all in a thread and then I can just link to the thread (or individual screenshots), and can add to it as more come up 🙂 P.S. feel free to reply with more

I hereby present to you, AI's greatest 5hits...

@RoRo
I'm a high school Maths teacher/tutor, if that's of any help (I've found trying to change things in a school to be extremely difficult - the "we've always done it this way" mentality - so not sure I can help you much in that regard). All my Maths posts are made using the #MathsMonday hashtag (and various other Maths hashtags, but you can find all of my specific ones under MathsMonday, which only a couple of other teachers have ever used here)