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It often happens that two or more similar values are distinguished with the ' symbol, e.g. a, a', a'' and similar. How is this pronounced?

Felix Dombek
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    Note that through the joys of Unicode we now have an actual prime symbol so you can do a′ now instead of using an apostrophe for the job. There are even double prime ″ and triple prime symbols ‴. (OK there are still lots of times you might still have to use an apostrophe - the future ain't perfect yet.) – hippietrail May 23 '11 at 01:57

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A' would typically be called A prime; A'' would be called A double prime and so on.

waiwai933
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As @waiwai933 said, the answer is A prime, A double prime, ans so on. As usual, Wikipedia has more details. In French (and probably other languages), double prime, triple prime, and so on are named seconde (2nd), tierce (an old word for 3rd). According to wikipedia, it was the same in English before the 1960s (but the relevant sentence is tagged with [citation needed]).

This progression is indeed the etymological origin of the symbol, which was initially a superscript Roman number.

Frédéric Grosshans
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    In Polish, we use prim, bis, and ter (from Latin), which makes reading such expressions very fast (saying "x bis" instead of "x double prime"). For higher orders we would probably say "fourth derivative of" etc. – dolphin Mar 12 '24 at 02:25
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In my father's generation, this was "a dash" in the UK, but I think "a prime" has overtaken this since.

Colin Fine
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    In my UK generation (left school in 1985 with double-maths A-levels) f'(x) was read as f dash of x and f''(x) was f double-dash of x. But I'd understand "prime" too. – Phil M Jones Oct 21 '15 at 08:15
  • @PhilMJones and ColinFine: In my UK generation (left school in 2003 with double-maths A-levels) this was still "a dash". I vaguely recognise "a prime". – AndyT Mar 08 '17 at 15:05
  • I left school in 1974. I can't now be sure, but I think that I knew it as "a prime". – Colin Fine Mar 08 '17 at 18:42
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I encountered this ' in the context of vector math referred to as a dash in the book Support Vector Machines which you can read about at http://www.support-vector.net/nello.html published by Cambridge University press. I have never encountered this usage before. The use is in the math appendix, example B-2.

"We use a dash to denote transposition of vectors (and matrices) so that a general column vector can be written as..."

mcwizard
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We read a' as "a dash" in Japan. However, "a prime" is occasionally used in universities. At its explanation of the word prime, the Oxford English Dictionary VIII (1970) states that a' is "usually read 'a dash', etc." I think the tendency that "dash" is changed to "prime" is caused by LaTeX (or troff), which is used from 1980s and in which a' is formatted as a^\prime (or a opprime).

Community
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H. Kato
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    That’s odd.  I’ve been doing mathematics in the US since before TeX existed and before troff was widely known (is it widely known now?), and I’m sure I’ve never referred to a′ as “a dash.”  I’m fairly sure I’ve always called it (and heard it called) “a prime.”  Can you provide a link to the OED comment? P.S. a^\prime doesn’t look like troff notation to me. – Scott - Слава Україні Mar 07 '17 at 03:25
  • @Scott-san: I don't doubt that "a prime" is common in US, neither tell that "a dash" is correct. I only want to show that there are several variants. The link of OED is not available because I can only access the printed books in the library of my University. However, similar explanation can be found in Longman Dictionary of the English Language (1985), which states "Br prime" in the explanation of "dash". – H. Kato Mar 08 '17 at 09:36