SmartmanApps

23

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

You’re using different screenshots this time?

Nope. Exact same page I already referred you to before, page 23.

Well done, you’ve progressed to ones that include the word

Just like the ones that include the word "Product", eh? 🤣🤣🤣 Well done for reading beyond 1 sentence this time by the way. Now go back to the other ones and read beyond 1 sentence - you've just shown you're capable of it

unfortunately you seem to have forgotten the task

Not me - the difference between axb is Multiplication, as per page 23, and ab is a Product, as per page 36. Still waiting on you doing your task of explaining how they give 2 different answers when, according to you, they are "the same thing" 🙄

14

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

In your screenshot of a textbook, they refer to it as a convention twice

Left to right is a convention, yes, doing Multiplication and Division before Addition and Subtraction is a rule 🙄

And you still haven’t explained prefix or postfix notation not having order of operations

For the 3rd time it does have order of operations 🙄 You just do them in some random order do you? No wonder you don't know how Maths works

Get rekd idiot

says person who doesn't know the difference between conventions and rules, and thinks postfix notation doesn't have rules 🙄

25

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

Not important

Says person who said...

None of the screenshots you put in that reply even use the word “multiplication”,

So let me help you out...

It’s an example, not explicit.

It explicitly says "Multiplication" at the bottom of the page! 😂

If I asked for an explicit reference for the meaning of the word “table”, a source that discusses carpentry but never uses the word itself is not explicit

And this page does use the word "Multiplication". Are you seeing yet why I kept telling you to read more than 2 sentences? 😂

Do you need me to explain in more detail what “explicit” means?

Do you need me to explain in more detail what "read more than 2 sentences" means?

I, for one, am content that there is no such explicit reference for your interpretation of the meaning of the word multiplication

And yet there it is, right there on page 23. Who would thought? Oh yeah, people who have read more than 2 sentences out of the whole book 😂

Your second reference says “when multiplications are denoted by juxtaposition, as in 4c ÷ 3ab”. Very interesting.

Yeah, 1912 textbooks are "very interesting", much more so than modern textbooks which never call it such 😂

Maybe we can discuss that after you demonstrate it’s worth it

I already pointed out the problem with your not reading more than 2 sentences out of a textbook again there

“other rules than those just described might have been adopted” which, again, is interesting

It's not actually, if you know the history behind that comment, which I have no doubt that you don't

27

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

None of the screenshots you put in that reply even use the word “multiplication”

So what do you call 10x3, exactly? I'll wait 😂

so they are certainly not saying explicitly that ab is not a multiplication

They are saying explicitly that bc is a Term, and goes entirely into the denominator, not c into the numerator like in a/bxc does.

that a multiplication is different from a product

So, according to you, c going into the denominator, and c going into the numerator, are somehow not different 🤣🤣🤣 a/bxc, where c goes in the numerator, and a/bc, where c goes in the denominator, go ahead, explain it to me like I'm 5, how are they the same thing according to you 🤣🤣🤣

This level of reading comprehension is what got you here

says person who can't tell the difference between a/bxc=axc/b, and a/bc=a/(bxc) 🤣🤣🤣

I’m sure you were wise enough to put your best attempt first

Hey, I was restricting it to the same textbook like you said. If you wanna go ahead and open it up to other textbooks , then explain how a/bxc=16 and a/bc=1 are the same thing , I'll wait. 🤣🤣🤣 I've never encountered anyone who has claimed 1 and 16 are the same thing, so go ahead and explain it to me 🤣🤣🤣

29

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

You’re still not doing any of the very simple things to demonstrate that it’s worth having a discussion with you

says person still not reading the posts where I did 🙄

Feel free to start

Been doing it the whole time dude. You're the one ignoring the textbooks that prove you are wrong 🙄

then I can get back to reading fully

There's nothing stopping you doing that now

Yes, you need to do them in a short comment.

So don't post so much BS in the first place and it won't turn into a long reply 🙄

Ok, here's something short for you, you said...

Where in your textbook does it say explicitly that ab is not a multiplication, or that a multiplication is different from a product in any substantive sense, eh?

Ok, so yet again you have ignored my repeated please to you to read more, but you have again refused, so this emabrassment is of your own making...

Page 23, a÷bxc=axc÷b...

Page 282, answers on Page 577, a÷b(c+d) is a over b(c+d), and not ax(c+d) over b 🙄

You going to reply now? Or just gonna ignore it as usual?

provide an actual textbook example where any of the disputed claims you make are explicitly made

It's in the actual textbook I already gave you, and you refused to read more than 2 sentences out of it 🙄

Where’s your textbook which says “ab is a product, not multiplication”?

Same textbook. See previous point.

there is a textbook reference saying “ab means the same as a × b

Yep, and does not say that they are equal, for reasons they are not equal,see above, from the very same textbook you kept lying about what it said 🙄

so your mental contortions are not more authoritative

I've just proven it was you who was making the mental contortions, as I have been telling you all along

your ability to interpret maths textbooks is poor

says person who claimed that "means" means "equals", in contradiction of the whole rest of the textbook 🙄

My prediction: you’ll present some implicit references

And just like everything else, you were wrong about that too, 🙄 but "oh no! too long! I'm not going to read that"

And here you are admitting to someone else what I have been telling you the whole time 🙄

While reading some of his linked textbooks I found examples which define the solidus as operating on everything in the next term, which would have 1/ab = 1/(ab) = 1/(ab) = 1/ab

This is also how we were taught though as I recall it was not taught systematically

Yes it is, literally every textbook, not just Maths, but Physics, Engineering, etc. and it's referenced in Cajori in 1928, they all use ab=(axb).

remember one teacher when I was about 17 complaining that people in her class were writing 1/a·b but should have been writing (1/a)·b

because (1/a) is 1 Term, a fraction, but 1/a is 2 Terms, 1 divided by a.

if you have a correct understanding of what the order of operations really are

rules

you can understand that these conventions all become a bit unwieldy when you have a very complex formula

not to anyone who knows all the rules 🙄

(ab)/(bc) not ((ab)/b)c (which is what the strict interpretation of PEMDAS

No it isn't. ab=(axb), so ab/cd=(axb)/(cxd), (axb) done in the P step, (cxd) done in the P step, then you do the division - it's not complicated! 😂 Literally every textbook in all subjects does it that way. That is the strict interpretation of PEMDAS 🙄

because “bc” just visually creates a single thing

a TERM. Come on, you can say it. 😂

even though bc(x-1)(y-1)·sin(b) is a single term

Nope! It's 2 Terms 🙄

Because DumbMan doesn’t understand mathematical convention

So, I just call you DumbMan from now on? Got it! 😂

looks like he’s gone to sleep again now

It's called having a life. So sorry to hear you don't have one

That won’t be a problem if you actually wanted to do it

I actually did it and you confessed to not reading it

Bye!

I'll take that as an admission of being wrong then., Don't let the door hit you on the way out.

11

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

That screenshot calls it a convention you troll

says the actual troll, who didn't notice it was talking about left to right,. which is indeed a convention which it is explaining 🤣🤣🤣

31

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

I’m pretty sure you already replied to it

Yep, and you admitted to not reading it 🙄

what you needed to do if you wanted to continue the discussion

And when I had, in your next comment you posted, you admitted you didn't read it 🙄 I even posted the screenshot of you saying that

I’ve read plenty of your nonsense by now

but admitted to not reading the proof that you were wrong 🙄

told you explicitly why I’m not reading more

What you said: too long

What you meant: not reading anything which proves I'm wrong

don’t get all weepy when I follow through.

says person who admitted to not following through 🤣🤣🤣

29

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

Your argument you haven’t made is backed up by math textbooks you haven’t provided written for children

That's quite a word salad. You wanna try that again, but make sense this time?

Your argument you haven’t made

If I didn't make it then it's not my argument, it's somebody else's 😂

is backed up by math textbooks you haven’t provided

as well as the textbooks I have provided 😂

written for children

All my textbooks are for teenagers and adults

How can that specific order of operations be a law of mathematics if it only applies to infix notation, and not prefix or postfix notations

I already addressed that here. I knew you were making up that I hadn't addressed something 🙄

Laws of mathematics are universal across notations

Correct, they do.

also says that order of operations is a law of mathematics.

If you think it's not a Law, then all you have to do is give an example which proves it isn't. I'll wait

You don’t have it

You mean you don't have a counter-example which proves it's not a Law

you also aren’t a maths teacher

says liar

Just because you say it a lot doesn’t make it true.

You know you just saying it's not true doesn't make it not true, right? 🤣🤣🤣

BTW, going back to when you said

8÷2x4 PEMDAS: 8÷2x4 = 8÷8 = 1

Here it is from a textbook I came across this week which proves I was right that you did it wrong 😂

Therefore, doing Multiplication first for 8÷2x4 is {(8x4)÷2}, not 8÷(2x4) - whatever you want to do first, you write first - exactly as I told you to begin with 🙄

33

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

I explained why here

And you were proven wrong elsewhere (since you ran your rubbish to the maximum comment depth), but admitted to not reading it, speaking of proving you were the bad faith one all along 🙄

So, now that I've found a place I can reply to your other non-repliable posts...

Even if you corner them on something

Which no-one ever has 🙄

they absolutely will not budge

See how many Mathematicians and Maths teachers you can gaslight into believing that they and Maths textbooks are all wrong, I'll wait.

I like many others brought up calculators and how common basic calculators only evaluate from left to right

And you hilariously provided a manual that proved you were wrong about that! 😂

He asserted (without evidence) that the first does not operate in this way

It's right there in the manual, as I pointed out 😂

even though the manual says that you must re-order some expressions so that bracketed sub-expressions come first

That's right, because it doesn't have brackets keys 🙄 So you have to enter that first, then press the equals key to make it evaluate that first, because it doesn't evaluate from left to right otherwise, it will do the multiplication first 🙄

still will not admit that he was wrong about his claim

says person who still will not admit he was wrong about his claim that all basic calculators working that way, even though the manual proves there are some that don't 😂

you will not convince him of anything no matter what the evidence is

Says person refusing to believe all evidence, including the calculator manual 😂

he fundamentally cannot separate mathematics from the notation

Nope liar. I'm the one who keeps pointing out they are different 🙄 Go ahead and find a screenshot of me saying they're the same, I'll wait

He calls a×b multiplication and ab a product.

As per Maths textbooks, which you keep ignoring 🙄

These are, of course, the exact same thing

says person who not only can't give a single textbook which says that, but refused to answer my question about

For a=2, b=3

1/ab=1/(2x3)=1/6

1/axb=1/2x3=3/2

which of those, according to you, is the correct answer, given you insist they are "the same thing" 🙄

implicit multiplication

There's no such thing. Go ahead and find a Maths textbook that says so, I'll wait

ab can, by some conventions, have a higher precedence than does the explicit multiplication in a×b

Literally always does, as per the rules of Maths, as found in Maths textbooks 🙄

he has taken that to mean that they are fundamentally different

So go ahead and explain how "the same thing", according to you, can give different answers in all textbooks. I'll wait

He thinks that a(b+c)=ab+bc is something to do with notation

The Distributive Law actually, another rule of Maths 🙄

not a fundamental relationship between multiplication and addition

There's no multiplication in The Distributive Law, only in The Distributive Property 🙄

I will say that no author would distinguish those two terms

Except, of course, for all the ones who do 😂

because they’re just too easily confused

says person confused about the difference between a Law and a Property 😂

And many authors explicitly say that one is also known as the other

says person who can't even cite a single example of such

He says that a×(b+c) = ab + bc is an instance of the “distributive property”

ax(b+c)=axb+axc actually.

You seem to think notation is only correct at exactly the level you claim to teach

Nope, every level after Primary school

Elementary school children get taught parentheses means you do stuff inside parentheses first

Because they haven't been taught The Distributive Law yet, and there is no outside brackets for them - they don't learn that until Year 7

college calculus students get taught parentheses mean you do stuff inside parenthesis first

No they don't.

despite two centuries of textbooks showing that is in fact how parentheses work

You're the one ignoring the 2 centuries of textbooks dude 😂

All published textbooks and all pragmatic mathematics operate as though your pet peeve does not exist

says person who can't cite a single such example, again 🙄

It’s almost like the shit you insist upon is completely made-up, and does not matter to anyone besides you

says person who actually made up that Multiplication and Products are the same thing 🙄

I thought they were called “products” not “multiplications”

That's right. You know you're referring to a 1912 textbook, right? Terminology has moved on since then, as demonstrated by the 1965 textbook 😂

I’m just trying to give you more opportunities to prove that you’re not just a troll

says person who ignored all the textbooks I posted, whilst not citing any themselves 🙄

You insist you’re talking about mathematical rules that cannot be violated, so it should be no problem to find an explicit mention of them

I provided many, which you ignored 🙄

you are saying that the practice of calculators, mathematical tools, programming languages and mathematical software are all wrong

Nope, liar. All my calculators give correct answers (Sharp, Casio, Omron - only Texas Instruments breaks the mold these days), and programmers disobeying the rules of Maths doesn't prove they not rules of Maths. 🙄 You are the one claiming that Sharp and Casio calculators are giving wrong answers. 🙄 I'm guessing that your calculator, if you even have one (which seems doubtful from what I've seen) is a Texas Instruments one.

that you are right

My caclulators and textbooks are correct, yes. 🙄

that my interpretation of your own textbooks is wrong

says person who read one sentence and stopped there and did some mental gymnastics with it, ignoring that the whole rest of the book contradicts that interpretation 🙄

if you show no ability to admit error

says the person who actually made errors.

admit that disagreement from competing authorities

There isn't any "disagreement from competing authorities". 😂 Every single textbook, not just Maths, but Physics, Chemistry, Engineering, etc., obeys the exact same rules 😂

As my own show of good faith, I

didn't look at any of the examples about Distribution and Terms, speaking of proving you are the bad faith person 🙄

I’ll explain why I think this is a bad convention

and you would be wrong, just like you are about everything else

why the formal first-order language of arithmetic doesn’t have this convention

No-one cares why a niche topic, only taught at University, is different to the general rules taught to everyone at high school 🙄

the distributive law is something you must do instead of a property of multiplication that you can use to aid in the manipulation of algebraic expressions but don’t have to

That's right, as per Maths textbooks

Folded into their inability to understand that some aspects of maths are custom and convention

Says person who has an inability to tell the difference between a convention and the rules 🙄

Somewhere along the way he seems to think that distributivity is something to do with brackets instead of something to do with addition and multiplication

Law Vs. Property, not complicated!

if I can get him to actually cop to any of his verifiable mistakes

Of which there are none as opposed to you who has several verifiable mistakes 🙄

back up any of his whackadoodle claims with direct references

You've been given them, and you ignored them

Tomorrow I’m expecting another wall of text responding to every single word except the ones where I ask for such an admission

says person who has still failed to show anywhere that I was mistaken 🙄 On the other hand you have refused to admit to your mistakes

I’ll have satisfied myself he’s a lost cause

Actually, you admitted to not even reading it - that's something which people who know they are wrong do 🙄

been pushing his wrong ideas of what the distributive law are, since 2023

says person again ignoring the Maths textbooks 🙄

Notice how the text never says “you MUST use the distributive law”?

I notice how you have comprehension and/or honesty issues

It always says some variation of “in order to simplify, you must…”?

Which part of the word "must" don't you understand? 😂 Also, which part of simplifying Brackets is part of the order of operations don't you understand? 😂

No, you don’t notice, because you’re blind

cough cough 😂 Here's another one, in case you're still in any doubt...

don’t understand what distributivity actually is.

says the person who actually doesn't understand what The Distributive Law is

You also got me confused with someone else trying to explain in short words how you’re wrong

Nope. Tweedle Dum and Tweedle Dee say very similar things, but one can still tell them apart.

bye

Don't let the door hit you on the way out! 😂

1

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 3mo ago

Microsoft lessons are like this...

1

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 4mo ago

Have to reply to your other post here, because you hit the maximum comment depth with your rubbish.

I thought they were called “products” not “multiplications”

That's right, as per Page 36 of Modern Algebra, published in 1965, as opposed to Advanced Algebra, published in 1912., but if you think we still call it "Multiplication" you're more than welcome to find a modern textbook which calls it that, instead of relying on a 113 year old textbook 🙄

If you can find an explicit textbook example where writing a(b)²

What did you not understand about textbooks write ab² if they meant (axb²)?

that’s another way you can prove your good faith

I already proved it with all my other textbook references, which you keep ignoring 🙄

the exponent could be anything other than 1

In other words, you refuse to believe the rule that I have already quoted multiple times, because it proves you are wrong about this meme, and so trying to derail the argument, still, with your false equivalence argument, speaking of lacking good faith 🙄

Likewise, if you can find any explicit textbook example which specifically mentions an “exception” to the distributive law

There aren't any exceptions. I'm not sure why you're having trouble with that. You want me to find evidence of something I have said all along doesn't exist 😂

I’m not saying that such an explicit example is the only way to demonstrate your claim

says person who to date has refused to accept what any textbook has said about it 🙄

I’m just trying to give you more opportunities to prove that you’re not just a troll

Since when do trolls post Maths textbooks backing them up? 🤣🤣🤣

that it’s possible to have a productive discussion.

says person who has rejected literally every Maths textbook I've posted. 🙄

You insist you’re talking about mathematical rules that cannot be violated

as per Maths textbooks 🙄

so it should be no problem to find an explicit mention of them

...and I already posted many of them, but for some reason you find them unacceptable (that reason being that they prove you are wrong 😂 )

you should remember that you are saying that the practice of calculators, mathematical tools, programming languages and mathematical software are all wrong

Nope, liar. All calculators except for Texas Instruments and e-calcs are correct - certainly all my calculators are correct (as can be seen in the video in the thread). Same thread shows the reason that programmers are almost all wrong - they don't even all get it wrong in the same way - everyone gets it wrong in different ways, which debunks the whole idea of them following any rules 😂

that my interpretation of your own textbooks is wrong

Which you would've found out for yourself, had you read more than 2 sentences out of them. 🙄 Welcome to what happens when you only read the scaffolding part of a lesson, and not the new content part of the lesson 🙄

if you show no ability to admit error

says person who has failed to admit their error about the calculators. 🙄For me to do so would require me having made an error to begin with, which I haven't, which is why you've been unable to say where I've made an error 🙄

to admit that disagreement from competing authorities casts doubt on your claims

There isn't any disagreement from competing authorities, and yet you still refuse to admit you're wrong 🙄

to evince your controversial claims with explicit examples that are not subject to interpretational contortions,

says the only person who has made such contortions, such as "means" means "equals" 🙄

the likelihood is that you’re not willing to ever see truth

You you mean, as evidenced by the fact that you had already dismissed me as being good faith in your above post before I had even seen THIS post - something, something, judge, jury, and executioner 🙄

there’s no point arguing with such a person

I'm not arguing with you - I'm debunking your rubbish claims lest any reader fall prey to them

sorry for making multiple replies on the same point

Which at the end of it all you had still failed to make a point.

As my own show of good faith, I do see that one of your textbooks (Chrystal) has the convention that a number “carries with it” a + or -, which is suppressed in the case of a term-initial positive number

No, a show of good faith by you would be 1. accepting that axb and ab are different, as per the page you reference above, which I'll come back to in a tick, 2. accepting The Distributive Law, a(b+c)=(ab+ac), is a thing found in many Maths textbooks (all of which you ignored), otherwise all you have conceded was yet another side-quest on your part because you refuse to concede anything which is actually relevant

So, you started this post with referencing Page 6 of Advanced Algebra (as proven by you quoting the bit about "Multiplication", which explicitly shows that bxc and bc ARE NOT THE SAME THING, and yet here you are still not acknowledging this fact.

a÷bxc=12÷3x4=16, a÷bc=12÷(3x4)=1

I’ll explain why I think this is a bad convention

It's not a convention, it's a rule 🙄

why the formal first-order language of arithmetic doesn’t have this convention

No-one cares 🙄 Most people don't go to university and learn niche rules, everyone goes to high school and learns the general rules

You failed to demonstrate any good faith

says the person who actually demonstrated no good faith 🙄 and was unable to back up anything they said with a textbook

so this is the end of this conversation

Don't let the door hit you on the way out

Your reply reveals that you even understand that you were wrong

Nope!

“it’s designed that way”

Yep, that shows I was correct about "simple" calculators, whereas chain calculators were designed that way, but that was used as moving goalposts by the person claiming this applied to "simple" calculators, which was disproven by the manual showing that it did indeed have a stack and obey the order of operations rules, hence the goalposts got moved, again 🙄

the language changed

You think it doesn't change?? BWAHAHAHAHAHA 🤣🤣🤣 But sure, Mr. I'm (not) showing good faith, go ahead and show us a modern textbook which calls Products "Multiplication". I'll wait. 😂 Oh wait. you said the conversation was over. Too bad you can't prove your point then... again

but are so prideful,

Correct is the word you're looking for

so averse to ceding ground,

says person who has failed to come up with a single valid point that I could therefore cede to 🙄

that you just… can’t… say it!

says person who has failed to admit they are wrong about things they have been proven wrong about 🙄

The children you really ought to stop teaching are more mature than this.

They're more mature than you yes. They have no problem at all with The Distributive Law and why it exists, and can see their calculators know this also.

You’re an embarrassment to the profession.

says the actual embarrassment who can't back up anything they say with any Maths textbook 🙄

31

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 4mo ago

Man, this whole post has been embarrassing for you

Nope. I'm the only one who has backed up what they've said with Maths textbooks 🙄

I can’t help but notice youve once again failed to address prefix and postfix notations.

What is it that you want addressed?

And that you’ve not actually made any argument other than “nuh uh”

Backed up by Maths textbooks 🙄

We can all tell you’re not a maths teacher

Says person who actually isn't a Maths teacher, hence no textbooks 😂

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 4mo ago

You have a masters but you can’t differentiate between notation and the concept it is trying to convey

By which you mean you mean you don't have a Masters and can't differentiate between notation and rules 🙄

33

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 4mo ago

A “teacher” who doesn’t know that all lessons are simplifications that get corrected at a higher level,

As opposed to a Maths teacher who knows there are no corrections made at a higher level. Go ahead and look for a Maths textbook which includes one of these mysterious "corrections" that you refer to - I'll wait 😂

refers to children’s textbook as an infallible source of college level information

A high school Maths textbook most certainly is an infallible source of "college level" information, given it contains the exact same rules 😂

A “teacher” incapable of differentiating between rules of a convention and the laws of mathematics

Well, that's you! 😂 The one who quoted Wikipedia and not a Maths textbook 😂

A “teacher” incapable of looking up information on notations of their own specialization

You again 😂 Wikipedia isn't a Maths textbook

36

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 4mo ago

I love how confident you are about something you clearly have no knowledge of.

says person confidently proving they have no knowledge of it to a Maths teacher 🤣

At least if we’re judging by word count

from Maths textbooks, which for you still stands at 0

2

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 4mo ago

My dude sit in a university lecture for math majors

You know I have a Masters in Maths, right? 🤣

Your school books arent gospel

Proofs are, and these things are very easy to prove 🙄