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Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

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July 26th, 2019, 01:36 PM   #11
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Originally Posted by DarnItJimImAnEngineer View Post
Dogma and principles aside, I think we can all agree with that one, no?
My reply got a little longwinded. tl;dr: I realize that I always over-paren when I'm coding. I never realized before today that I have to over-paren when I'm writing ASCII math. It's a shock to my system. Original post follows.

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 "right-associative" 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 over-parenthesize 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 left-associates 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 right-associates.

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 over-parenthesize 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. Left-associativity will be abolished. Till then ... "Today I learned."

Last edited by Maschke; July 26th, 2019 at 02:07 PM.
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