Talk:Division by zero

message: — Assignment last updated by Annie.nguyen0811 (talk) 21:33, 27 October 2022 (UTC)
thread_title: Wiki Education assignment: Computer Science Principles

message: In Paragraph "Algebra" there ist written:
"It follows from the properties of the number system we are using (that is, integers, rationals, reals, etc.), if b ≠ 0 then the equation a/b = c is equivalent to a = b × c. Assuming that a/0 is a number c, then it must be that a = 0 × c = 0."
This is wrong, since the assumption b ≠ 0 is already violated in the next sentence. Stephan Schief (talk) 20:15, 8 May 2023 (UTC)
replies: text: The statement that the denominator of a fraction cannot be equal to zero in the number systems mentioned is a correct statement, but the sentence saying that is awkward enough so I can understand how it can be misread. I'll try to make it clearer. Rick Norwood (talk) 10:32, 9 May 2023 (UTC)
replies: text: I agree that in the field structure of the reals (or rationals), if b≠0, then a/b=c implies a=b×c. But one can not use this argument to say that if a/0=c, then a=0×c. Because then one would use b=0, in contradicition to the assumption. Stephan Schief (talk) 10:50, 9 May 2023 (UTC)

text: As I'm sure you know, when showing something by way of contradiction, it is standard to violate the assumption, arrive at a contradiction, and so demonstrate that the assumption is correct. I've tried to rewrite the paragraph so make the hypothetical nature of the claim clearer. Rick Norwood (talk) 11:04, 9 May 2023 (UTC)
replies: text: I did not realise that you were using an argument by contradiction! I am sorry about that. I like how you rewrote the paragraph, it is a lot clearer to me now. Thank you! Stephan Schief (talk) 11:13, 9 May 2023 (UTC)
thread_title:  Error in Paragraph "Algebra" 

message: I'm trying to rewrite the lead section for clarity, but I don't think I've done an amazing job so far. Does anyone want to take another crack at it, or maybe polish up some of my sentences? For example, can someone improve this vague sentence I wrote without making it too long or technical? "When a real function involves division by a quantity that can become zero for some values, that is a type of singularity." @XOR'easter? –jacobolus (t) 19:47, 7 December 2023 (UTC)
replies: text: Is that sentence necessary? I don't think the body text follows up on it in any serious way (unlike the concept of a limit in the next sentence). XOR'easter (talk) 20:03, 7 December 2023 (UTC)

text: Similarly, I think we should try to get the historical coverage right in the main text and then do a summary in the lead, rather than polishing lines in the lead that aren't elaborated upon later. XOR'easter (talk) 20:10, 7 December 2023 (UTC)

text: I like discussing the limit of 1/x in the intro before bringing up indeterminate forms. XOR'easter (talk) 21:03, 7 December 2023 (UTC)
thread_title:  Lead section 

message: I think this section would be better titled something like "other number systems", since the focus is the extended real numbers and the projectively extended real numbers, and the material about Wheel theory could be moved there.
It should IMO be preceded by a section (perhaps titled "Calculus") discussing the treatment in calculus and real analysis of the limits of functions with real numbers as the domain/codomain, where infinity is often treated as a limit but not a number per se. This section would discuss infinite singularities, and possibly contrast them with other kinds of singularities, and would then include material about indeterminate forms and L'Hospital's rule.
It might be worth adding a section about complex analysis and the idea of zeros and poles and meromorphic functions. –jacobolus (t) 23:20, 7 December 2023 (UTC)
replies: text: I think "Calculus" is a more illuminating section heading than "Analysis". The former refers to a specific math subject (and even people who haven't studied it have heard of it as a math thing), whereas the latter has a general meaning of "thinking about" that could be confusing in this case. XOR'easter (talk) 00:12, 8 December 2023 (UTC)
thread_title:  "Analysis" section 

message: if a/b=c then cb=a, right?
then, 0/0=0
as 0*0=0.
anyone find any sources for this?49.37.202.122 (talk) 16:07, 5 January 2024 (UTC)
replies: text: I realise my mistake. 0/0 is 0, 1, i, and every number. 49.37.202.122 (talk) 16:14, 5 January 2024 (UTC)

text: going from cb = a to a/b = c is only valid if b<>0. Dhrm77 (talk) 16:15, 5 January 2024 (UTC)
thread_title:  0/0 = 0 

message: I split this section up and rewrote the first part (the second half, now titled 'Inverse of multiplication') still needs a rewrite). Does it make sense to folks? This kind of informal discussion about concrete interpretations of division and the way zero might fit in seems valuable to me to include up front, but I'm just one person here. Hopefully it doesn't seem like belaboring the point or getting to far into the weeds. I'll try to find and insert a few relevant reliable sources if I can. –jacobolus (t) 01:41, 7 January 2024 (UTC)
replies: text: @XOR'easter (or anyone else reading along) do you mind giving the first half of this article another once-over? I tried to add some more accessible examples and informal discussion, but I can't promise it makes more sense to anyone other than myself. –jacobolus (t) 01:40, 10 January 2024 (UTC)
replies: text: Looks OK to me. XOR'easter (talk) 03:23, 10 January 2024 (UTC)
thread_title:  rewritten "meaning of division" section 

message: In the "Elementary arithmetic" section; "The meaning of division" - there is, and I quote: "Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle 1:0}" - I suppose a mathematical function was put there, but has failed for reasons beyond my comprehension. I hope someone may be able to fix it? Or was it only on my browser? I used two browsers and both showed this error.
Althuios (talk) 14:58, 29 April 2024 (UTC)
replies: text: These errors are transient, and there's nothing editors can really do about them. –jacobolus (t) 15:15, 29 April 2024 (UTC)
thread_title:  Seems to be an error.