Poll: 6÷2(1+2)
- Thread starter Barks
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Yes but there are still arbitrary standards that we follow
2x^2 being 2(x^2) and not (2x)^2
a/bc is technically (a/b)c or ac/b and not a/(bc)
this is a known source of confusion when using the / or ÷ operators and the reason why this question has caused so much fuss - there is however a standard way to use those operators regardless of the silliness of the question
Wow!
That is pretty intimidating. I was a bit of a chancer when I did my humble BSc, you are obviously extremely dedicated to maths. I wish I had the time to spend on learning more (and refresh my memory on things like PDEs). I was considering doing a masters through OU but I ended up spending time on learning IT stuff like Citrix instead :/So you are AlphaNumeric right? I think I still have the PDF you made of the 0.9r proofs.
a/bc is not technically (a/b)c as it is commonly understood to mean a/(bc) and the reason it is commonly understood to be that is due to the question being phrased ambiguously. Please read up on ambiguity.
Link for ambiguity
Sorry but this is the same argument as this very thread and we do have a convention for '/' it isn't ambiguous if you stick with convention. It does have potential to confuse so parenthesis should be used for the sake of clarity though there is still only one meaning technically.
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That would be me. That document I wrote before Wikipedia existed and which I used to learn LaTeX. Now I have to stop myself from typing LaTeX into forums when I want to talk maths \frac{like}{this}So you are AlphaNumeric right? I think I still have the PDF you made of the 0.9r proofs.
My job is now working on various areas of mathematics which I otherwise wouldn't have ever done if I'd stayed in academia so I'm fortunate in that sense. I'd still be focusing on the tiny tiny area my thesis pertained to, while now I've had to learn a wider range of things, from more in-depth functional analysis through to optimisation. That and I'm actually doing useful maths now, there's not a chance in hell my PhD will ever be experimentally tested.
The practical effect is that you should never write an expression like a/bc unless you are sure it won't generate any confusion -- e.g. if you can be certain your audience will infer from context whether you mean (a/b)c or a/(bc). That is what the question is doing and you cannot infer what it is implying.
Cos its not even wrong
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Totally agree and you should never write an expression as per the OP - it doesn't prevent us from using standard convention rigidly to answer it.
Problem is, without knowing the expression writers intentions, you might get the "right" answer to the wrong question.
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This is why mathematicians use better notation. I mentioned in my last post I have to stop myself typing LaTeX code when I want to put maths here. If I wanted to say (ab)/c) then I'd type \frac{ab}{c}. If I wanted to do a/(bc) I'd do \frac{a}{bc}. That makes the expression unambigious. It's considered extremely bad practice to type a maths paper (or even lecture notes really) in LaTeX and use / as a divisor. By using this proper pseudo-code in LaTeX you remove any ambiguities. I often write emails in LaTeX code, when communicating with other mathematicians, as you get to the point where you can 'compile' it in your head and thus the structure of the code helps you avoid such ambiguities.
There's plenty of conventions in mathematics which are designed to avoid these issues. For instance, you don't write (sin x)(sin x) as sin x^2, you write it as sin^2 x. This removes the confusion with sin(x^2).
In many textbooks you'll see the author say something like "Let K be a [something]" and later on "Let K be [something else]" but then they immediately follow it with "Except where there might be confusion, in which case I'll write the expression in full detail". These sorts of practices and issues with ambiguity become second nature after a while. Hence why I find this entire thread a bit daft. Anyone sufficiently versed in mathematics to know about associativity, commutativity, rings, fields, algebras (no not algebra, algebras), groups etc is going to be almost conditioned to not write such dubious expressions as the one in the thread title. The sorts of people who write such expressions are unlikely to be playing by the strict rules of mathematics, else they'd not make such a 'mistake' and thus you'd have to ask them what they meant.
Henceforth the answer is either 1 or 9.
If I replaced with variables, for arguments sake, and placed it in a practical context the question is utterly meaningless in its current format.
a÷b(c+b) = x
That could mean anything unless you knew its intentions as stated.
Well the intention is clearly to troll in this instance tbh.. as this question or a variant of it has been plastered around the internet.
Regardless of that its already known there is potential for confusion with / or ÷ operators however there are still standard ways to use these operators. You can still answer the question.
Out of interest, what sort of stuff do you do now?
this is the whole point hes trolled you basically its a masterclass troll there is no right or wrong answer.
he obviously knew of the sum the outcome that why it was posted lol
6/2(1+2) = x
6/2 = (1+2)x
3 = 3x
1 = x
2(1+2) is one term.
a/b(z+y) = x
a/bz+by = x
a = (bz+by)*x
a = (2+4)*1
a = 6*1
a = 6
No matter how many times I do this equation, I'll get the same answer - 1.
I can't comprehend why anyone would get a different answer, perhaps there's something else to it that I hadn't been taught on A-levels nor GSCE. Uni studies never raised this problem either. Which is not a problem at all, TBF.
The answer would be different if there was a multiplication sign between the bracket and the second term as you would be calculating from left to right.
6/2 = (1+2)x
3 = 3x
1 = x
2(1+2) is one term.
a/b(z+y) = x
a/bz+by = x
a = (bz+by)*x
a = (2+4)*1
a = 6*1
a = 6
No matter how many times I do this equation, I'll get the same answer - 1.
I can't comprehend why anyone would get a different answer, perhaps there's something else to it that I hadn't been taught on A-levels nor GSCE. Uni studies never raised this problem either. Which is not a problem at all, TBF.
The answer would be different if there was a multiplication sign between the bracket and the second term as you would be calculating from left to right.
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