💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @ SmartmanApps @programming.dev

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591

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2 yr. ago

That you’re still wrong?

About? You haven't pointed out anything that's wrong.

the problem is written poorly due to the obelus and thus is open to interpretation

Oh, you're one of those people. Good, maybe we can finally get an answer then (this was also talked about in the blog). What other interpretation of an obelus is possible other than division? People keep saying it's ambiguous, but no-one has ever said why (other than some stuff that makes no sense in the context, as explained in the blog)

The distributive property is sometimes called the distributive law of multiplication and division

Yes, and sometimes people call Koalas "Koala bears", but that doesn't mean they're bears. Now bearing that in mind, read again what Khan said - the page which is called "Distributive property explained", not "Distributive Law explained".

Wait till you hear that “i before e except after c” wasn’t true either

Wait till you hear that's not a rule of Maths.

It’s wild that you think 7th grade math overrules grad school math though

Umm, never said anything of the kind...

And...? Not sure what your point is, but the link is VERY badly worded...

1. The Distributive Law and The Distributive Property aren't the same thing - he's applying The Distributive Law, but mistakenly calling it The Distributive Property (a lot of people make that mistake). The latter is merely a property in Maths (like the commutative property, the associative property, etc.), the former an actual rule of Maths The Distributive Law
2. Applying the Distributive Law - i.e. expanding brackets/parentheses - is part of solving brackets. i.e. the first step in BEDMAS/PEMDAS. There's no "once you've used", you've already started!
3. As I already said, this is taught in Year 7, so I'm not sure what your point is?
   

Even more ambiguous math notations

Except that isn't ambiguous either. See my reply to the original comment.

Geogebra has indeed found a good solution

Geogebra has done the same thing as Desmos, which is wrong. Desmos USED TO give correct answers, but then they changed it to automatically interpret / as a fraction, which is good, except when they did that it ALSO now interprets ÷ as a fraction, which is wrong. ½ is 1 term, 1÷2 is 2 terms (but Desmos now treats it as 1 term, which goes against the definition of terms)

What’s |a|b|c|?

The absolute value of a, times b, times the absolute value of c (which would be more naturally written as b|ac|). Unlike brackets, there's no such thing as nested absolute value. If you wanted it to read as the absolute value of (a times the absolute value of b times c), then that's EXACTLY the same answer as the absolute value of (a times b times c), which is why nested absolute values make no sense - you only have to take absolute value once to get rid of all the contained signs.

If you’d ever taken any advanced math, you’d see that the answer is 1 all day

Don't need to do advanced Maths - every rule you need to know for this problem is taught in Year 7.

It's totally clear. It's a number divided by a factorised term, as per The Distributive Law and Terms.

It's the first, as per The Distributive Law and Terms. It could only ever be the second if the 6/2 was in brackets. i.e. (6/2)(1+2).

Indeed it was already solved more than 100 years ago. The issue isn't that it's "ambiguous" - it isn't - it's that people have forgotten what they were taught (students don't get this wrong - only adults). i.e. The Distributive Law and Terms.

No, it doesn't. It never talks about Terms, nor The Distributive Law (which isn't the same thing as the Distributive Property). These are the 2 rules of Maths which make this 100% not ambiguous.

Yeah, base ten really screws around with programming. You specifically have to use a decimal type if you really want to use it (for like finance or something), but it's much slower.

Also noted that you've declined on taking on that bet I offered.

somewhere

You know EXACTLY where I said those things, and you've been avoiding addressing them ever since because you know they prove the point that #MathsIsNeverAmbiguous See ya.

Sources are important not just for what they say but how they say it, where they say it, and why they say it.

None of which you've addressed since I gave you the source. Remember when you said this...

you can’t identify authors, you can’t check for bias

So, did you do that once I gave you the link? And/or are you maybe going to address "what they say but how they say it, where they say it, and why they say it" in regards to the link I gave you?

You keep reiterating your point as if it is established fact,

What they teach in Maths textbooks aren't facts? Do go on. 😂

tell me how it supports you

I did, and you've apparently refused to read the relevant part.

in comparison to a Phd

You know not all university lecturers do a Ph.D. right? In which case they haven't done any more study at all. But I know you really wanna hang on to this "appeal to authority" argument, since it's all you've got.

I have no interest in continuing this discussion

Yeah I saw that coming once I gave you the link to the textbook.

including the ‘highschool’ math

...when they were in high school.

teach the same (or similar) curriculum each and every year

There you go. Welcome to why high school teachers are the expert in this field.

math textbooks as the ultimate solution and so, so many of them are written by professors

So wait, NOW you're saying textbooks ARE valid in what they say? 😂

I want to point out that your only two sources

All that points out is that you didn't even read THIS thread properly, never mind the other one. Which two are they BTW? And I'll point out which ones you've missed.

I assume you accepted that seeing as you did not respond to that point

Well, I'll use your own logic then to take that as a concession, given how many of my points you didn't respond to (like the textbook that I gave you the link to, and the Cajori ab=(ab) one, etc.).

I’ve given 3 sources,

3 articles you mean.

all of which you dismiss simply because

...all of them have forgotten about The Distributive Law and Terms., which make the expression totally unambiguous. Perhaps you'd like to find an article that DOES talk about those and ALSO asserts that the expression is "ambiguous"? 😂 Spoiler alert: every article, as soon as I see the word "ambiguous" I search the text for "distributive" and "expand" and "terms" - can you guess what I find? 😂 Hint: Venn diagram with little or no overlap.

I could probably find some highschool textbooks that support weak juxtaposition if I searched,

Do you wanna bet on that? 😂

without ever providing a source that explains these rules

They're in my thread, if you'd bothered to read any further. By your own standards, 😂I'll take it that you concede all of my points that you haven't responded to.

I expect you to have a mathematical proof for why weak juxtaposition would never work, one that has no flaws. Otherwise, at best you have a hypothesis

You know some things are true by definition, right, and therefore don't have a proof? 1+1=2 is the classic example. Or do you challenge that too?

So do YOU have a hypothesis then? How "weak juxtaposition" could EVER work given "strong juxtaposition" is the only type ever used in any of the rules of Maths? I'll wait for your proof...

without providing evidence for your own position

You know full well it's all in my thread. Where's yours?

I’m saying I shouldn’t have to go looking

You didn't have to go looking - you could've just accepted it at face-value like other people do.

You’ve provided a single textbook,

No, multiple textbooks. If you haven't seen the others yet then keep reading. On the other hand you haven't provided any textbooks.

the argument is that both sides are valid and accepted

But they're not. The other side is contradicting the rules of Maths. In a Maths test it would be marked as wrong. You can't go into a Maths test and write "this is ambiguous" as an answer to a question.

here’s an article from someone who writes textbooks

Not high school textbooks! Talk about appeal to authority.

Yep, seen it before. Note that he starts out with "It is not clear what the textbook had intended with the 3y". How on Earth can he not know what that means? If he just picked up any old high school Maths textbook, or read Cajori, or read Lennes' letter, or even just asked a high school teacher(!), he would find that every single Maths textbook means exactly the same thing - ab=(axb). Instead he decided to write a long blog saying "I don't know what this means - it must be ambiguous".

Not only that, but he also didn't know how to handle x/x/x, which shows he doesn't remember left associativity either. BTW it's equal to x/x² (which is equal to 1/x).

the ambiguity exists

...amongst people who have forgotten the rules of Maths. The Maths itself is never ambiguous (which is the claim many of them are making - that the Maths expression itself is ambiguous. In fact the article under discussion here makes that exact claim - that it's written in an ambiguous way. No it isn't! It's written in the standard mathematical way, as per what is taught from textbooks). It's like saying "I've forgotten the combination to my safe, and I've been unable to work it out, therefore the combination must be ambiguous".

You are correct, I suppose a mathematics professor from Harvard (see my previous link for the relevant discussion of the ambiguity) isn’t at the high school level.

Thank you. I just commented to someone else last night, who had noticed the same thing, I am so tired of people quoting University people - this topic is NOT TAUGHT at university! It's taught by high school teachers (I've taught this topic many times - I'm tutoring a student in it right now). Paradoxically, the first Youtube I saw to get it correct (in fact still the only one I've seen get it correct) was by a gamer! 😂 He took the algebra approach. i.e. rewrite this as 6/2a where a=1+2 (which I've also used before too. In fact I did an algebraic proof of it).

the ambiguity exists and one side is not immediately justified/‘correct’

The side which obeys the rules of Maths is correct and the side which disobeys the rules of Maths is incorrect. That's why the rules of Maths exist in the first place - only 1 answer can be correct ("ambiguity" people also keep claiming "both answers are correct". Nope, one is correct and one is wrong).

That’s a leading question and is completely unhelpful to the discussion.

Twice I said things about it and you said you didn't believe my interpretation is correct, so I asked you what you think he's saying. I'm not going to go round in circles with you just disagreeing with everything I say about it - just say what YOU think he says.

Here you go - I found I did save a screenshot of Cajori saying ab and (ab) are the same thing - I didn't think I had.

In fact you're not allowed to add the multiplication - it breaks up the factorised term, hence gives a different answer.

The rule is you're not allowed to add dots (multiplication) - broke up the factorised term, which is why a different answer.

ChatGPT says...

Only if it's a fraction. If it's 2 separate terms then you use whatever your country uses for division - obelus or colon or whatever. They have to be 2 separate things, otherwise how would you write to divide by a fraction?