I'll take that as an admission that you're wrong then. Bye now.
P.S. someone else just provided me with even more things which are wrong in it. Even more glad I didn't waste time reading the rest of it.
SmartmanApps
joined 1 year ago
Notation isn’t semantics
Correct, the definitions and the rules define the semantics.
Mathematical proofs are working with
...the rules of Maths. In fact, when we are first teaching proofs to students we tell them they have to write next to each step which rule of Maths they have used for that step.
Nobody doubts that those are unambiguous
Apparently a lot of people do! But yes, unambiguous, and therefore the article is wrong.
But notation can be ambiguous
Nope. An obelus means divide, and "strong juxtaposition" means it's a Term, and needs The Distributive Law applied if it has brackets.
In this case it is: weak juxtaposition vs strong juxtaposition
There is no such thing as weak juxtaposition. That is another reason that the article is wrong. If there is any juxtaposition then it is strong, as per the rules of Maths. You're just giving me even more ammunition at this point.
Read the damn article
You just gave me yet another reason it's wrong - it talks about "weak juxtaposition". Even less likely to ever read it now - it's just full of things which are wrong.
How about read my damn thread which contains all the definitions and proofs needed to prove that this article is wrong? You're trying to defend the article... by giving me even more things that are wrong about it. 😂
I stopped reading it when I found it was wrong., and said what was wrong about it. You have still not said where mine is allegedly wrong. I'll take that as an admission that you're wrong then.
Ok so you’re saying it never happened, but then in the very next sentence you acknowledge that you know it is happening with TI today
You asked me what I do if my students show me 2 different answers what do I tell them, and I told you that has never happened. None of my students have ever had one of the calculators which does it wrong.
that both behaviors are intentional and documented
Correct. I already noted earlier (maybe with someone else) that the TI calculator manual says that they obey the Primary School order of operations, which doesn't work with High School order of operations. i.e. when the brackets have a coefficient. The TI calculator will give a correct answer for 6/(1+2) and 6/2x(1+2), but gives a wrong answer for 6/2(1+2), and it's in their manual why. I saw one Youtuber who was showing the manual scroll right past it! It was right there on screen why it does it wrong and she just scrolled down from there without even looking at it!
none of these calculators is “wrong”.
Any calculator which fails to obey The Distributive Law is wrong. It is disobeying a rule of Maths.
there is no ambiguity where there actually is.
There actually isn't. We use decimal points (not commas like some European countries), the obelus (not colon like some European countries), etc., so no, there is never any ambiguity. And the expression in question here follows those same notations (it has an obelus, not a colon), so still no ambiguity.
i recommend reading this one instead: The PEMDAS Paradox
Yes, I've read that one before. Makes the exact same mistakes. Claims it's ambiguous while at the same time completely ignoring The Distributive Law and Terms. I'll even point out a specific thing (of many) where they miss the point...
So the disagreement distills down to this: Does it feel like a(b) should always be interchangeable with axb? Or does it feel like a(b) should always be interchangeable with (ab)? You can't say both.
ab=(axb) by definition. It's in Cajori, it's in today's Maths textbooks. So a(b) isn't interchangeable with axb, it's only interchangeable with (axb) (or (ab) or ab). That's one of the most common mistakes I see. You can't remove brackets if there's still more than 1 term left inside, but many people do and end up with a wrong answer.
By “we” do you mean high school teachers, or Australian society beyond high school?
I said "In Australia" (not in Australian high school), so I mean all of Australia.
Because, I’m pretty sure the latter isn’t true
Definitely is. I have never seen anyone here ever use a colon to mean divide. It's only ever used for a ratio.
Do you have textbooks where the fraction bar is used concurrently with the obelus (÷) division symbol?
All my textbooks use both. Did you read my thread? If you use a fraction bar then that is a single term. If you use an obelus (or colon if you're in a country which uses colon for division) then that is 2 terms. I covered all of that in my thread.
EDITED TO ADD: If you don't use both then how do you write to divide by a fraction?
You can’t prove something with incomplete evidence
If something is disproven, it's disproven - no need for any further evidence.
BTW did you read my thread? If you had you would know what the rules are which are being broken.
the article has evidence that both conventions are in use
I'm fully aware that some people obey the rules of Maths (they're actual documented rules, not "conventions"), and some people don't - I don't need to read the article to find that out.
You haven't told me where it's wrong yet. I already said where the article is wrong.
Indeed Duncan. :-)
his rule could be replaced by the strong juxtaposition
"strong juxtaposition" already existed even then in Terms (which Lennes called Terms/Products, but somehow missed the implication of that) and The Distributive Law, so his rule was never adopted because it was never needed - it was just Lennes #LoudlyNotUnderstandingThings (like Terms, which by his own admission was in all the textbooks). 1917 (ii) - Lennes' letter (Terms and operators)
In other words...
Funny enough all the examples that N.J. Lennes list in his letter use
...Terms/Products., as we do today in modern high school Maths textbooks (but we just use Terms in this context, not Products).
I have never encountered strong juxtaposition
There's "strong juxtaposition" in both Terms and The Distributive Law - you've never encountered either of those?
unable to agree on an universal standard for anything
And yet the order of operations rules have been agreed upon for at least 100 years, possibly at least 400 years.
unscientific and completely ridiculous reason refuse to read
The fact that I saw it was wrong in the first paragraph is a ridiculous reason to not read the rest?
Let me just tell you one last time: you’re wrong
And let me point out again you have yet to give a single reason for that statement, never mind any actual evidence.
you should know that it’s possible that you’re wrong
You know proofs, by definition, can't be wrong, right? There are proofs in my thread, unless you have some unscientific and completely ridiculous reason to refuse to read - to quote something I recently heard someone say.
try not to ruin your students too hard
My students? Oh, they're doing good. Thanks for asking! :-) BTW the test included order of operations.
Noted that you were unable to tell me what The Distributive Law relates to (given your claim it's not brackets).
Skimmed your comment and it’s wrong
So tell me where it's wrong.
Let me know if you ever decide to read the article instead of arguing against an imagined opponent
There's nothing imaginary about the fact that he claimed it's ambiguous, and is therefore wrong. Tell me why I should read a wrong article, given I already know it's wrong.
When I discovered this comment I went to read it, and yes, it's true you discussed the Distributive Property, however, what these people are talking about is The Distributive Law which isn't the same thing (though people often call it the wrong name), and makes the question completely unambiguous. You literally can't move on from the "B", Brackets, in the rules until there are no brackets left - the B is literally short for "solve Brackets" (every letter is "solve (something)"), and so anyone who does the division before solving the brackets has just violated the order of operations rules.