
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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July 26th, 2019, 01:36 PM  #11  
Senior Member Joined: Aug 2012 Posts: 2,409 Thanks: 753  Quote:
Say I'm on a nice site like this that supports $\LaTeX$. When I write $a^{b^c}$, it is universally recognized (according to Wiki) that this is "rightassociative" as they call it. We interpret it right to left. On the other hand, say I'm on a site that doesn't support $\LaTeX$; or, to be precise, MathJax, which is the gizmo that makes $\LaTeX$ work on websites. So I revert to ASCII and I write a^b^c. That should not make any difference. But it does. It's not that I was unaware of some programming language exceptions. I just never regarded the exceptions as truly legitimate before today. I overparenthesize whenever I program in a language I'm not super familiar with. Perhaps I've internalized that lesson without thinking about it. But for me it's the MATLAB thing. MATLAB is a serious computational system. Professional scientists use it. If someone leftassociates exponentiation, I can no longer regard them as wrong or ignorant. The usage is regarded as legitimate when the ^ symbol is involved. And yet there's Wolfram Alpha, the gold standard for all things computational. Wolfram rightassociates. And I was surprised at the number of programming languages that interpret $4^2$ as $16$. That seems deeply wrong to me. But again, I admit that when I'm coding, I do overparenthesize just in case. Even if I'm familiar with the language's conventions, I can't be sure a reader of the code agrees. But that issue is different. The exceptions are only for programming languages and spreadsheets (and calculators). But with exponentiation, the exceptions can occur even when discussing math in ASCII. I do find that disturbing and never before today regarded that as remotely legitimate. When I'm emperor, this is going to get fixed. Leftassociativity will be abolished. Till then ... "Today I learned." Last edited by Maschke; July 26th, 2019 at 02:07 PM.  

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exponent, negative, power 
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