What does (the string of characters) that looks like this- apple- mean to you?

Should be

What do (the string of characters) that look[/B]) like this- apple- mean to you?

"string of characters" is plural.

Yawn.

What if you have more than one string of characters? Is it pluralplural?

"Look- a line of ants!"
"Look- two lines of ants!"
"Look- a breakfast table with a quantum buddhist!"
"Look- two breakfast tables with 5 Hooters girls!"

"Look- someone is trying to apply logic in a discourse with UtH!"
"Ooooooooh noooooooooooooes!"

Textbook, please. From where I sit it's equally possible (and frankly a whole lot more likely) that it was 'taught to you like that' and you've either learned it wrong or forgotten it.

Quote:

(b) Some people argue about arithmetic-operation precedence by
referring to what this or that calculator or programming language
does. However, I believe all such references are irrelevant; for what
may be syntactically convenient for some computing device need not be
convenient (or traditional) for human mathematical writing.

So? You don't think my proposed measure of consensus is relevant; that's not the same as a counterexample.

(I'd say it is relevant, for the same reasons economisto gave. Computers are how math gets done for real world purposes. If they're all doing it wrong, we're all screwed. If two or more syntactic conventions were genuinely acceptable then don't you find it a bit odd that someone, somewhere, would not have designed a language that uses the other one, or that lets you pick which convention to use?)

Quote:

(c) They have to teach one of the methods don't they ? They can choose either one, as either is correct/acceptable.

I did say "practiced", not "taught". Even so, you are wrong. Where there are competing conventions (e.g. in calculus, y-dot vs y-prime vs dy/dt) we teach all of them. Here there aren't.

Quote:

Referring you a little closer to home, try the American Mathematical Society and their views.

The American Mathematical Society, rather unsurprisingly, does not have an official position on the order of arithmetic operations. Similarly it has no official position on the existence or otherwise of imaginary numbers.