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I’m talking about the classic 4/2x. If x = 2, it is:
4/2x2 = 2x2 = 4
4/(2x2) = 4/4 = 1
It's the latter, as per the definition of Terms. There are references to this definition being used going back more than 100 years.
Wolfram solved this with going with the second if it is an X or another variable as it’s more intuitive
Yes, they do if it's 2x, but not if it's 2(2+2) - despite them mathematically being the same thing - leading to wrong answers to expressions such as the OP. In fact, that's true of every e-calculator I've ever seen, except for MathGPT (Desmos used to handle it correctly, but then they made a change to make it easier to enter fractions, and consequently broke evaluating divisions correctly).
how do you calculate 2(1+1)? It’s 4. It’s called implicit multiplication
No, it's not called implicit multiplication. It's distribution.
We could write this up as +2*(+1+(+1))
No, you can't. Adding that multiplication has broken it up into 2 terms. You either need to not add the multiply, or add another set of brackets if you do, to keep it as 1 term.
I can’t think of a situation where it’s incorrect
If a=2 and b=3, then...
1/axb=3/2
1/ab=(1/6)
If there is a letter or number or anything next to a bracket, it’s multiplication
No, it's distribution. Multiplication refers literally to multiplication signs, of which there aren't any in this expression.
2x is the same as 2*x
No, 2A is the same as (2xA). i.e. it's a single Term. 2xA is 2 Terms (multiplied).
If a=2 and b=3, then...
axb=2x3 (2 terms)
ab=6 (1 term)
This guy talks in hashtags.
Only in the first post in each thread, so that people following those hashtags will see the first post, and can then click on it if they want to see the rest of the thread. Also "this guy" is me. :-)
Grab a calculator, look at wolfram docs, ask a professor or teacher
I'm a Maths teacher with a calculator and many textbooks - I'm good. :-) Also, if you'd clicked on the thread you would've found textbook references, historical Maths documents, proofs, the works. :-)
8/2(2+2), let’s remove the confusion
8/2*(2+2), brackets
8/2*(4), mult & div, left -> right
4*(4), let go
2 mistakes here. Adding the multiplication sign in the 2nd step has broken up the term in the denominator, thus sending the (2+2) into the numerator, hence the wrong answer (and thus why we have a rule about Terms). Then you did division when there was still unsolved brackets left, thus violating order of operations rules.
it’s more like 8/(2x), but it’s just harder to read, so we don’t
But that's exactly what we do (but no extra brackets needed around 2x nor 2(2+2) - each is a single term).
you could argue that it should be handled like the scenario with the x
Which is what the rules of Maths tells us to do - treat a single term as a single term. :-)
there are no rules of this
Yeah, there is. :-)
you use fractions instead of inline division
No, never. A fraction is a single term (grouped by a fraction bar) but division is 2 terms (separated by the division operator). Again it's the definition of Terms.
And by all means, correct me if I’m wrong
Have done, and appreciate the proper conversation (as opposed to those who call me names for simply pointing out the actual rules of Maths).
link something that isn’t an unreadable
No problem. I t doesn't go into as much detail as the Mastodon thread though, but it's a shorter read (overall - with the Mastodon thread I can just link to specific parts though, which makes it handier to use for specific points), just covering the main issues.
as long as we are civilised
Thanks, appreciated.
No, you demonstrably didn't understand mine, which is, what you are saying is impossible, but you're still saying it's possible.
No, you can't. You already tried to do addition first in 2+3x4 and found out why it doesn't work. Ever since then you've been ignoring that result and pretending that there's some other way to make it work. No, there isn't. As long as multiplication is defined in terms of addition (i.e. 3x4=3+3+3+3) then it's impossible to get a right answer unless you do multiplication before addition.
No, you can't. Again, you already proved you can't.
Go ahead - I'm not holding my breath. I already told you why it literally can't work. But note that adding brackets isn't changing the order of operations - brackets are already part of the order of operations. Writing 2+3x4 as 2+(3x4) is exactly the same thing.
BTW just to FURTHER prove your "addition first" doesn't work, look at this example...
3x4+2=3x6=18. But earlier you did 2+3x4=5x4=20 - not even the same answer in an "addition first" world! Welcome to why it's impossible to make addition-first work. But knock yourself out - you're welcome to try! 😂
No, it isn't. It's part of the rules of Maths. Notation is how you write it - underlying that is how Maths actually works. This is embodied in the rules of Maths.
Completely fixed, and a result of the way the operators are defined - that was the only "arbitrary" bit, deciding what the operators were and what they were going to mean, but once you did that then the order of operations rules were already written for you (having already been determined as soon as you made the definitions of the operators in the first place).
Again, not a convention, a rule of how to interpret it. You can't just decide to interpret 5 as four, or again, you end up with wrong answers. The rules of Maths prevent you from getting wrong answers. You found that out yourself when you tried to do addition first in 2+3x4.