Which of the following sentence is irrefutable?

Question

Which sentence is correct?

The expression 0/0 is undefined.
The expression "0/0" is undefined.

What is the part of speech of "expression" and "0/0" in this sentence?

*irrefragable* has been almost totally replaced by *irrefutable* over the past couple of centuries (few native speakers today will ever have used it themselves, and most probably wouldn't even know of the earlier word). So I suggest you avoid it. — FumbleFingers, Aug 26 '20 at 11:49
@FumbleFingers Okay, I edited the question. It was just an impulsive decision to use it. Please answer my question. — Niraj Raut, Aug 26 '20 at 12:03
I would say they're both irrefutably undefined, absent any context. — Hot Licks, Aug 26 '20 at 12:11
If something is undefined, can it even be an expression (or anything at all)? — Hagen von Eitzen, Aug 26 '20 at 12:18
I don't know the answer to your actual question. I'd say "Parts of Speech" is a bit of a blunt instrument anyway, but would you be prepared to call both terms "nouns"? What use is it to have syntactic labels at this level? (I mean the level at which it might make a difference whether some term is set off by quote marks or not.) — FumbleFingers, Aug 26 '20 at 12:21
...do you see any difference between your specific example and, say, The surname Smith* is common in the US*? — FumbleFingers, Aug 26 '20 at 12:26
@NSR If you have to call them anything at all, call them nouns. And I agree with FumbleFingers, using quote marks doesn't make any difference here. — , Aug 26 '20 at 12:30
@FumbleFingers: Let me propound to you what I think in plain, elaborate language: Whenever we use a reference to an object, which in this case is "the expression" and proceed to make the object it (the reference) refers to explicit by mentioning the object itself, then we must bound the object made explicit with commas (regular or inverted). Please tell me whether my scrutiny is correct. — Niraj Raut, Aug 26 '20 at 12:31
@Hagen Von Eitzen-- I think "expression' is an acceptable term here. — , Aug 26 '20 at 12:31
@Hagen von Eitzen Isn't it just like saying "The sentence is incorrect"? — Niraj Raut, Aug 26 '20 at 12:33
At least part of this question is to do with the "use-mention" distinction. In which context the earlier question Is there punctuation for words treated as words? may be relevant. — FumbleFingers, Aug 26 '20 at 12:51
@NSR plain, elaborate language gave me a good chuckle: protip, the harder you try to sound erudite, the less plausible it is (see what I did there?). — Dan Bron, Aug 26 '20 at 13:55
As a math teacher I'd like to observe that we don't usually put quotation marks around mathematical expressions. The word "expression" is a noun, and 0/0 is not really a part of speech, although I guess we could think of it as the words "zero divided by zero." — Chaim, Aug 26 '20 at 14:52
I'm also confused why the title asks whether the question is "irrefutable." Are you asking the mathematical question whether one can refute the claim that 0/0 is undefined? Or are you asking a question about the use of punctuation marks and about parts of speech? — Chaim, Aug 26 '20 at 16:00

score 1 · Accepted Answer · answered Aug 26 '20 at 14:43

The expression xyz is a string containing an announcement of a quote (in the widest sense of that word, something one wishes to display) and the actual quote.

Quotes are traditionally offset by quotation marks, as in direct speech:

She shouted "Can you manage to swim across?"

Here, I'd prefer italics to offset a non-word expression, but 0/0 looks weird rather than highlighted. 0/0 is distinct enough, though adding offset quotes thus: '0/0' is not too unkind on the eyes and follows some old convention obediently. I usually prefer a horizontal bar, which demands a mathematical font.

The rules of grammar and punctuation are somewhat different in the maths domain. I'd probably stick here with

Division by zero is not a feasible operation, so 1/0, 3·142/0 and 0/0 etc are undefined.

Which of the following sentence is irrefutable?

1 Answers1