What does the symbol marked by the arrow represent?
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Akiva Weinberger
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Rajesh Marndi
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2It looks to me like a misprinted $=$ sign. – MJD Feb 06 '23 at 05:29
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@MJD Really? How exactly would one digitally "misprint" an equal sign in such a fashion? – Philosophiæ Feb 06 '23 at 06:36
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8I'm guessing it's a misprinted ≠ sign. Perhaps a font is missing the / character used to turn = into ≠. – Greg Martin Feb 06 '23 at 06:50
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@Philosophiæ it is well known that pdf writers and readers can have errors. To explain how it happens, one needs to first understand what a pdf file is and explain how pdf files try to contain the required portions of the font files used for what writing appears. If edits occur after having created the font files and characters which weren't previously included are now used, the font file may not have been able to be altered... the renderer tries to find the corresponding letter in a related font family, but for symbols like math symbols, they don't always match. – JMoravitz Feb 06 '23 at 13:20
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A longer story shorter... it can be hard to make pdf files correctly and it is very easy to mess up. Such mistakes might not even be visible to the original author and only manifest when attempted to be viewed on a computer with fewer fonts natively available. – JMoravitz Feb 06 '23 at 13:23
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@Philosophiæ There could be a second character that is supposed to be overstruck with the $=$ sign, such as a slash or vertical bar, which is instead being rendered as a rectangle. Rendering unrecognized characters and unavailable glyphs as open rectangles is very common in software. – MJD Feb 06 '23 at 15:42
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@Philosophiæ For example: What do you call the phenomenon where a rectangle □ is shown because a font lacks a glyph? – MJD Feb 06 '23 at 15:55
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Indeed, on my own computer I'm unable to see certain symbols properly on this site. For whatever technical reason, $\mathcal{ABC}$, say, gets rendered as $\square\square\square$. – Théophile Feb 06 '23 at 15:55
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@Théophile Right-click on the broken formula, and select “Math Settings > Math Renderer > Common HTML” – MJD Feb 06 '23 at 15:56
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@MJD Oh! That fixes it. I just wonder why that would have changed a few weeks ago when it had been working fine for the past 10 years... Anyway, thank you! – Théophile Feb 06 '23 at 15:59
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@Théophile I don't know either, but further details are available at Why using \mathcal command produce a square?. – MJD Feb 06 '23 at 16:00
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@MJD Okay, it seems connected to the recent MacOS update. Makes sense. – Théophile Feb 06 '23 at 16:01
1 Answers
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I think Greg Martin's suggestion that it is a $\ne$ sign is clearly correct. The slash in the $\ne$ has been mistakenly rendered as a rectangle instead. As I mentioned, this is a typical sort of error in computer typesetting.
If it were $\ne$, the mathematics would be (almost) correct. For example, in the third bullet point, there are two cases: a circle if $A=C$, and an ellipse if $A\ne C$. It appears to be discussing the discriminant of a conic section; compare Wikipedia's treatment.
I did not pick up on this sooner because the first line would say $\Delta\ne 0$ but then in the second bullet point, $B^2-4AC=0$ would imply $\Delta=0$. I guess that this is an editing error.
MJD
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