💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @ SmartmanApps @programming.dev

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591

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2 yr. ago

I think I’m gonna trust someone from Harvard

So you're going with the appeal to authority argument - ok, got it.

But if you're gonna do that then make sure you check out Cajori's credentials, since that's, you know, who we both quoted.

argue with some of the actual mathematicians in here

You mean the dude who claimed to be, and was quoting wikipedia? BWAHAHAHAHA

It doesn’t seem that hard to just teach it as BEADMAS, where the A refers to numbers adjacent to variables

Terms already are taught!

Source?

Cajori (1928) for starters, plus any old Year 7 Maths textbook, any era (we know from Lennes letter that textbooks were already doing this in 1917).

Usually you’d use a fraction bar, which groups it and makes it unambiguous

Division (operator) and fraction bar (grouping symbol) aren't the same. It already is unambiguous.

Only way to get 1 is to violate left to right on multiplication and division

Actually the only way to get 16 is to ignore one of more rules of Maths - sometimes it's Terms, sometimes it's The Distributive Law, but always something. If you follow all the rules of Maths you get 1.

[…] the question is ambiguous. There is no right or wrong if there are different conflicting rules. The only ones who claim that there is one rule are the ones which are wrong!

https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

Yeah nah. Actual Maths textbooks and proofs - did you not notice the complete lack of references to textbooks in the blog? It's funny that he mentions Cajori though, given Cajori has a direct reference to Terms #MathsIsNeverAmbiguous

The crappier calculator is the one generating the incorrect answer

Which would be the app written by the programmer who didn't check his Maths was correct, as opposed to the calculator made by a company who, you know, makes calculators.

2x works the way it does because there’s a variable involved, and natural reading of that treats it as a single entity

Just like 2(2+2) is also a single Term.

no variables in the equation in the post, there are only definite numbers

Pronumerals literally stand in for numerals, and work exactly the same way. There is nothing special about choosing a pronumeral to represent a numeral.

8/2(2+2) is nothing more than 8/2×(2+2).

They're completely different actually. 2(2+2) is a single term in the denominator, (2+2) - which you separated from the 2 with an x - is a now 3rd term which is now in the numerator, having been separated from the 2 which is in the denominator.

There is nothing special about 2(…, this is not the equivalent of 2x

So what's it equal to when x=2+2?

2( is simply 2×(

No it isn't. 2(a+b)=(2a+2b) The Distributive Law

But there actually is only 1 right answer, and unfortunately for the person you're replying to it's 1.

Just proves, never too late to learn :-)

I would have got 1 by doing 2(2+2) = 8 first. Not because of bracket but because of “implied multiplication.”

Yeah, right answer but wrong reason. There's no such thing as implicit multiplication.

What I am learning here: 8÷2(2+2) is not same as 8÷2×(2+2)

Correct, and that's because of Terms - 8÷2(2+2) is 2 terms, with the (2+2) in the denominator, but 8÷2×(2+2) is 3 terms, with the (2+2) in the numerator... hence why people get the wrong answer when they add an extra multiply in.

number next bracket is not the same as normal multiplication in rule book

Right, because it's not "multiplication" at all (only applies literally to multiplication signs), it's a coefficient of a bracketed term, which means we have to apply The Distributive Law as part of solving Brackets.

÷ & × have right of way rule with whoever is left most wins

Yeah, the actual rule is Left associativity, and going left to right is the easy way to obey that.

There is a standard, I’m not claiming there isn’t

Ah ok. Sorry, got caught out by a double negative in your sentence.

Confusion exists because operating against the standard doesn’t immediately break everything like ignoring brackets would

Ah but that's exactly the original issue in this thread - the e-calc is ignoring the rules pertaining to brackets. i.e. The Distributive Law.

Ah ok. Well that was my only confusion was what you had actually intended to write, not how to interpret it (depending on what you had intended). Yes should be interpreted 2^81.

including Excel

Yeah, but Excel won't let you put in a factorised term either. It's just severely broken because the people who wrote it didn't bother checking the rules of Maths first. Programmers not knowing the rules of Maths doesn't mean Maths is ambiguous (it certainly creates a lot of confusion though!).

We have a standard because it’s ambiguous. If there was only one way to do it, we’d just do that,

Disagree. There is one way to do it - follow the rules of Maths. That's why they exist. The order of operations rules are at least 400 years old, and make it not ambiguous. If people aren't obeying the rules then they're just wrong - that doesn't make it ambiguous. It's like saying if e-calcs started saying 1+1=3 then that must mean 1+1 is ambiguous. It might create confusion, but it doesn't mean the Maths is ambiguous.

Yeah, didn't think that came from any textbook.

And also if I hadn't been replying to this thread then you wouldn't have got the proof that you were right. :-)

this a 4 month old thread

Yeah, I know, but it'll show up in search results for all eternity, and it's full of disinformation. As a Maths teacher/tutor who is sick of hearing "But Google/Wolfram/TI says...", I'm doing my best to try and get said people to fix their damn calculators (and also make people aware that those calculators are wrong. (sigh) I miss the old days when all calculators gave the right answer - what happened??). If you feel the same way then feel free to share my links - that's what they're there for. :-)

And right at the moment I'm feeling too tired to do anything which requires me to think about it, so just doing what I can do on automatic. ;-)

the difference in implicit vs explicit? It’s the same operation

"implicit multiplication" isn't even a real thing in Maths, and isn't even multiplication to begin with - people use that umbrella term to either mean The Distributive Law - which is the first step is solving Brackets - or Terms, which are products, which is the result of a multiplication.

e.g. if a=2 and b=3, then...

axb=2x3 - 2 terms

ab=6 - 1 term

Multiplication comes first, then division

They can be done in either order, or even together, as long as you go left to right.

Right idea, but wrong terminology.

There's no such thing as implicit multiplication

xy is a Term - Terms are separated by operators (none in this case) and joined by grouping symbols.

x(y) is a Bracketed Term, and is therefore subject to The Distributive Law, which is the first step in solving Brackets.

And yes, a multiplication symbol is an operator - which therefore separates Terms (which is why ab and axb aren't the same thing - it's 1 term vs. 2 terms), and the "M" in the mnemonics refers literally to multiplication signs, and nothing else.

but you’re supposed to read MD and as one step

You can do them in any order at all - M then D, D then M (hence the acronym BEDMAS), or all in one - what does matter is not treating Distribution as though it's Multiplication (which refers literally to multiplication signs), when in actual fact it's the first step in solving Brackets.

1 isn't ignoring anything. 16 can be arrived at by ignoring any one of multiple order of operations rules.