Because every single textbook you’ve cited, I absolutely guarantee it… was written in the past!
But being used in schools right now, and you're desperately trying to twist my words around to mean something else because you can't find any textbooks which say juxtaposition, except for one from 1912 🤣🤣🤣
How shall we make sense of this conundrum?
You're the only one who has issues with understanding present and past tense dude, you're the only one trying to use a 1912 textbook in the argument.
“I never use drugs” doesn’t mean the same as “I am not using drugs at the moment”
Yes it does, because "I never use drugs" isn't the same as "I have never used drugs" 🙄
So yeah, you absolutely said the wrong thing
I absolutely didn't Mr. I can only find it in a 1912 textbook 🤣🤣🤣
your reason for using it is stupid.
says person trying to bring a 1912 textbook into the argument only to avoid admitting having been wrong 🙄
If you were any kind of reasonable person and not someone incapable of admitting the slightest mistake
So not like you, which I'm not 😂
you would have said, “oh, sorry, I meant that textbooks don’t use the word ‘juxtaposition’ any more”
It's already there in the use of the present tense
Mate, try and keep track. We’re talking about a specific calculator and its specific manual.
And it specifically says you are wrong 🙄
Your calculator is not relevant to that one.
So when you said all, you didn't really mean all, so an admission that you were wrong about "all". Got it. Thanks for playing. Glad we're done with the "basic" calculator topic then
“Says person lying” is your favourite
statement of fact
deflection
says person talking about calculators that don't have brackets because he's absolutely proven wrong about The Distributive Law, and is trying to deflect away from admitting being wrong about that 🙄
the calculators we all had in primary school, If you press the following sequence of buttons: 2 + 3 x 5 =, the answer it will give is
17
even though they can make scientific calculator modes work correctly!
Nope! They don't! With the exception of MathGPT, they all ignore The Distributive Law, you know, the actual original topic 🤣🤣🤣 The Windows calculator in Scientific mode says 8/2(1+3)=16, because, when you type it in, it changes it to 8/2x(1+3). It's hilarious how you just keep making easily proven wrong statements and bring more embarrassment upon yourself, instead of just, you know, checking facts first 🤣🤣🤣
Sharp calculator obeying The Distributive Law
Note that neither MathGPT, nor the Sharp calculator, forcibly add in a multiply sign where it doesn't belong. Welcome to dumb programmer who has forgotten how The Distributive Law works and didn't bother checking in a Maths textbook first.
yet there’s such a simple explanation! They’re emulating basic four-function calculators that have existed for decades
No they're not! Just like they're also not emulating Scientific calculators that have existed for decades! 🤣🤣🤣
Do you see the contradiction between the following two statements
Nope!
Maths textbooks never use the word “juxtaposition”
Use of the present tense, no reference to the past at all
A textbook from1912
before you or I was even born
Need to work on your comprehension dude if you see a contradiction there
Is a textbook from 1912 not a textbook?
Does anything in what I said refer to textbooks in the past? That would be past tense, "have never used". Need to work on your comprehension dude
Does “never” mean something different where you’re from?
Is there no difference between past tense and present tense where you are from?
Your exact words were “Maths textbooks never use the word”.
Yep, exact use of present tense there
Do you stand by that statement now?
Yep
Do you want to admit it was incorrect?
Nope
This is actually even clearer than the lie
Not a lie. Nothing I have ever said is a lie
where you said you didn’t use different screenshots
Never said that either liar. Noted lack of screenshots, or have you still not worked out how to do that yet?
You get the same result if you don’t press the plus button at that point
No you don't! a+bxc and (a+b)xc aren't the same thing! 🤣🤣🤣
In what example in the manual
Unlike you I have an actual calculator, no need to look in manuals for how they work. Other dude posted a link where you can buy one for under $10. Go ahead and get one, and let me know what answer it gives you to 2+3x4. I'll wait 🤣🤣🤣
There is no such example
Hence I can confirm it on my own "non-scientific, non-graphing" calculator, unlike you who appears to not even own a calculator at all, and so is grasping at straws with online manuals 🤣🤣🤣
The annotated screenshot you keep posting is an example of left-to-right evaluation
No it isn't! It's an example of evaluating when you press the equals key 🤣🤣🤣 I knew you wouldn't admit to being wrong. 🙄
You’re just wrongly claiming that pressing the + button for the second time changes the behaviour of the manual
Says person lying about the += button, which acts as a + button when followed by a number, and as an = button when followed by anything else. Note that pressing it turns a+b into (a+b) and not a+b+ 🙄
You’re just wrongly claiming that pressing the + button for the second time changes the behaviour of the manual
says person lying about how a += button works 🙄
Your screenshot says that “calculations can usually be reconstructed as simple chains”
Yep, therefore it is a chain calculator, Mr. needs to go to remedial reading classes
You’re using that as evidence that the calculator is not a normal calculator
can't do that with a normal calculator, which you would know if you had one! 🤣🤣🤣
It’s so interesting that you couldn’t find anything in the manual saying, “this is a special kind of calculator”
says person lying about the screenshot saying you can use chains with it 🙄
A mystery.
It's not a mystery why you ignore what's in screenshots - can't admit to being wrong about anything 🙄 Your latest adventure involves pretending that present tense means past tense
Buddy, “chain calculators” as you call them are exactly the basic, four-function, stackless, cheapo calculators you can buy for three quid
says person revealing his lack of knowledge about different types of calculators, and also that he is lacking 3 quid to buy one and try it first hand
can’t admit that they’re normal,
says person who doesn't own a normal calculator, can't admit they aren't normal, because can't admit to being wrong about anything 🙄
I’m sure I have one lying around somewhere,
I'm sure you don't, or you wouldn't be hunting around online manuals desperately looking for something to twist into agreeing with you
Want to make a bet on what it’ll output?
with a proven liar. Nope. I'm sure you would go out and buy a chain calculator, then claim it was a "normal" calculator you just had lying around which you magically happened to find
It’s weird that your pettiness goes as far as not taking the W when it’s handed to you, dude
It's weird that you're pretending that you admitted to begin wrong about something when you didn't. Wait a minute, no it isn't. We've already established you're a gaslighter who can't admit to being wrong about anything 🙄
That’s some awful impressive goalpost shifting
BWAHAHAHAHAHAHA! Says person refusing to acknowledge that it's in textbooks the difference between conventions and rules 🤣🤣🤣
Gold medal mental gymnastics winner
Yep, I know you are. That's why you had to post known to be wrong blogs, because you couldn't find any textbooks that agree with you 🤣🤣🤣
And here you are, still unable to explain why prefix and postfix notation don’t have an operator precedence.
Speaking of goalpost shifting - what happened to they don't have rules?? THAT was your point before, and now you have moved the goalposts when I pointed out that the blog was wrong 🤣🤣🤣
I’m still waiting
says person who has still not posted any textbook at all with anything at all that agrees with them, to someone who has posted multiple textbooks that prove you are wrong, and now you are deflecting 🤣🤣🤣🤣
They literally don’t
they literally *do., That's why the rules get mentioned once at the start of the blog - it's the same rules duuuhhh!!! 🤣🤣🤣
I defy you to show me a single source that tells you that prefix or postfix notation use PEDMAS.
PEMDAS isn't the rules, it's a convention
I’ll even take Quora answers
I won't take anything but textbooks, and you've still come up with none
I’ll even take a reputable source talking about prefix/postfix that doesnt bring up how order of operations isn’t required for those notations.
That's exactly what the blog you posted does. I knew you hadn't read it! BWAHAHAHAHAHAHAHA! 🤣🤣🤣 I'll take that as an admission of being wrong then
No, you’ve show a screenshot from a random PDF
of a Maths textbook, with the name of the textbook in the top left, and the page number also in the top left. 🤣🤣🤣
Infix notation needs extra information to make the order of evaluation of the operators clear:
rules built into the language about operator precedence and associativity
Yep, says nothing about operator precedence being tied to the notation, exactly as I just said, so that's a fail from you then
But then you go on to say something to the effect of “anyone who knows the rules can the extra information”
derive the rules is what I said liar. The only thing you need to know is the definition of the operators, everything else follows logically from there.
Which is both unsubstantiated given the long history of not having PEDMAS
The order of operations rules are way older than PEMDAS. It even says it in one of the blogs you posted that PEMDAS is quite recent, again showing you didn't actually read any of it. 🙄
No, you’ve show a screenshot from a random PDF
Nothing random about it. The name of the textbook is in the top left. Go ahead and search for it and let me know what you find. I'll wait 🤣🤣🤣
What math textbook and what edition is it?
So, you're telling me you don't know how to look at the name of the PDF and search for it?? 🤣🤣🤣 I can tell you now it's the #1 hit on Google
The fact you think that factorization has to do with order of operations is shocking
says person revealing they don't know anything about order of operations 🤣🤣🤣 Make sure you let all the textbook authors know as well 🤣🤣🤣
Yes the multiplication is done first
No, Brackets are done first.
The law is about converting between a sum of a common product and a product of sums
Nope. That's the Distributive Property, and yes indeed, the Property has nothing to do with order of operations, but the Distributive Law has everything to do with order of operations.
No matter how you write them, it will always be about those things,
The Property will, the Law isn't
so the multiplication always happens first.
No, Brackets are always done first
It’s crazy that you’re not able to distinguish between mathematical concepts and the notation we use to describe them
says person who doesn't even know the difference between a Property and a Law, and, as far as I can tell, have never even heard of The Distributive Law, given they keep talking about the Property
But putting that aside, that’s not a proof of PEDMAS.
Right, it's a proof of the order of operations rules for Brackets 🙄
If PEDMAS is an actual law
It isn't, it's a convention
There are proofs for 1+1
It's true by definition. There's nothing complex about it. Just like ab=(axb) is true by definition
if PEDMAS is a law
It isn't, it's a convention. Not sure how many times you need to be told that 🙄
or an textbook snippet
You mean like textbook snippets stating that The Distributive Law is the reverse operation to Factorising?? See above 🤣🤣🤣
A claim entirely unsupported by the textbook example you provided
says person who pointed out to begin with it was talking about conventions. BWAHAHAHAHAHA! I even underlined it for you. Ok, then, tell me which convention exactly they are talking about if it isn't left to right 😂
Nowhere does it say that one is a convention
It quite clearly states that left to right is a convention 🙄
but not the other
"the other" wasn't even the subject at hand. 🙄 Here you go then...
it only says that removing brackets changes the meaning in some situations, which is fully within the scope of a convention
But not within the scope of rules 🙄
There you go again, just admitting you don’t know what postfix and prefix notations are.
There you go again not being able to say what the RULES for them are! 🤣🤣🤣 I admitted nothing of the kind by the way. I already told you 3 times they obey the same rules 🙄
here is a great free article from Colorado State university
It's pretty rubbish actually - finding a blog post by someone as ill-informed as you doesn't make it "great". Note that I always cite Maths textbooks and thus have no need to ever quote blog posts? 😂
Note how it says the rules about operator precedence are for the notation
Because (sigh) the same rules apply to all notations 🙄
which itself is a convention, as all notations are
Yep, and are separate to the rules, which are the same for all notations
Note how it says the rules about operator precedence are for the notation
Nope. Doesn't say that anywhere. Go ahead and screenshot the part which you think says that. I'll wait
how prefix and postfix don’t need those rules
Doesn't say that either. 🙄 Again, provide a screenshot of where you think it says that
BTW this is completely wrong...
"Infix notation needs extra information to make the order of evaluation of the operators clear" - Anyone who knows the definitions of the operators and grouping symbols is able to derive the rules for themselves, no need for any "extra information" 🙄
"For example, the usual rules for associativity say that we perform operations from left to right" - The thing we just established is a convention, not rules 🙄
"so the multiplication by A is assumed to come before the division by D" - Which we've already established can be done in any order 🙄
How embarrassing for you
No, you actually. You know, the person who can't find a single textbook that agrees with them 😂
Here are some more materials
NONE of which were Maths textbooks, NOR Maths teachers 😂
A post by Berkley university about popular ambiguous equations
None of which are actually ambiguous. He should've looked in a Maths textbook before writing it 😂
"the 48/2(9+3) question" - 48/2(9+3)=48/(2x9+2x3), per The Distributive Law, as found in Maths textbooks 😂
A published paper from Berkley that has been cited, with much stronger language on the matter
Did you even read it?? Dude doesn't even know the definition of Terms, ab=(axb) 🤣🤣🤣
Here is an article from the university of Melbourne
"Without an agreed upon order" - Ummm, we have proven rules, which literally anyone can prove to themselves 😂
Article from the university of utah
"There is no mathematical reason for the convention" - There are reasons for all the conventions - talk about admitting right at the start that you don't know much about Maths 🙄
A howstuffworks article on order of operations that explains it
It only explains the mnemonics actually, not why the rules are what they are. 🙄
Did you read it?? 🤣🤣🤣
"The order of operations — as Americans know it today — was probably formalized in either the late 18th century" - Nope! Way older than that 🙄
doesn’t have the pedigree of a university, but still clearly explained
It actually did a better job than all of the university blogs you posted! 🤣🤣🤣
Plus dozens of Quora answers, articles from online academies and learning centers, that I figured you’d just dismiss.
Because not Maths textbooks, duuuuhhhh 🤣🤣🤣
But to top it all off, if this was truely a law of mathematics
Which it is as per Maths textbooks 🤣🤣🤣
then show me a proof, theorem, or even a mathematical conjecture, about order of operations.
The proof is it's the reverse operation to Factorising, thus must be done first 🙄
But since you hate Maths textbooks, go ahead and search for "reverse operation of distributive law" and let me know what you find. I'll wait 🤣🤣🤣
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 🙄
“No one” in this context meant “no one who actually does maths professionally.”
No it doesn't. Everyone who does Maths professionally does it the same way as in Maths textbooks 🙄
When I see 1+½ i can instantly say “one and a half”
And that would be wrong. It's 1 plus one half. 1½ is one and a half.
when I see 1 + 1 ÷ 2 i actually have to pause for a moment to think about order of operations
You don't know to Divide before Adding??
one I recognize the structure of the problem immediately, and one feels foreign.
Says person with "decades of maths experience outside of textbooks" 🙄
The point is that people who do maths for a living
That would be me
are probably above average in maths, tend to write things differently than people who are stopped their maths education in high school (or lower)
Nope. We all write it the same way as we were taught, even those who have done Maths at University (also me).
these types of memes are designed around making people who know high school maths feel smart
No, they're designed around getting those who have forgotten the rules to argue about it. i.e. engagement bait
the order of operations is based on consensus and that any order could be used
No, as per example I gave, if you changed the order to addition first, you get a different answer (20 instead of 14), therefore demonstrably you can't use a different order of operations. You can only have a different order if you have different definitions of the operators to begin with... and again the order of operations would be derived from what definitions you used in that case.
I still think this claim is true
So you didn't understand the proof then.
your rationale is probably the basis for the current order of operations that we use
It's not my rationale - it's a mathematical proof. We started with 14. We therefore know any rules we make have to end up back at 14. Any rules which don't lead you back to 14 are demonstrably wrong and ruled out. That is the whole purpose of the rules of Maths in the first place - there is only 1 correct answer, and we have to have rules which can only give you that 1 answer when you follow them. It's the same thing the original authors of the order of operations would've done. There's no "consensus", there's just a Mathematician doing Maths and arriving at the rules which work. Then tells others what they are so that they don't have to go through working it out themselves (though some might if they want to confirm that what they've been told is correct. As I said, that's the beauty of Maths - you can do the Maths yourself and confirm that what you've been told is correct, like I just did).
But it doesn’t prevent us from using any other order of operations.
Of course it does. If you try using a different order of operations you no longer get 14 (as demonstrated when we do addition before multiplication with our current operator definitions).
which clearly states that the distributive property is a generalization of the distributive law
Let me say again, people calling a Koala a Koala bear doesn't mean it actually is a bear. Stop reading wikipedia and pick up a Maths textbook.
You seem to be under the impression that the distributive law and distributive property are completely different statements
It's not an impression, it's in Year 7 Maths textbooks.
this certainly is not 7th year material
And yet it appears in every Year 7 textbook I've ever seen.
Looks like we're done here.
If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous
The inverse of the function is f(x)^-1. i.e. the negative exponent applies to the whole function, not just the x (since f(x) is a single term).
P.S. feel free to read through and use my thread on order of operations.
Ok, that's a start. In your simple example they are all equal, but they aren't all the same.
yn+y - 2 terms
y(n+1) - 1 term
y×(n +1) - 2 terms
To see the difference, now precede it with a division, like in the original question...
1÷yn+y=(1/yn)+y
1÷y(n+1)=1/(yn+y)
1÷y×(n +1)=(n +1)/y
Note that in the last one, compared to the second one, the (n+1) is now in the numerator instead of in the denominator. Welcome to why having the (2+2) in the numerator gives the wrong answer.