Mark E. Shoulson via Unicode unicode at
Sat Nov 10 18:54:15 CST 2018

On 11/9/18 6:25 PM, Marius Spix via Unicode wrote:
> Dear Mark,
> I found another sample here:
> On page 86 it says that the aleph with diaresis is a number with
> the value 1000.

That's true, I've heard of that, and even occasionally seen it. And 
sometimes in old printings things like a diaeresis or a dot above were 
used where later Hebrew uses a U+05F3 HEBREW PUNCTUATION GERESH or 
U+05F4 HEBREW PUNCTUATION GERSHAYIM.  I think what struck me about this 
one was that this was not just something that looked like a 
diaeresis/umlaut, it really WAS an umlaut, a direct transcoding of the 
a-umlaut in Latin letters into aleph-umlaut in Hebrew letters.

> Yet another usage in a mathematical context of an aleph with umlaut can
> be found here, however they used U+2135 ALEF SYMBOL instead of U+05D0
> HEBREW LETTER ALEF. This is not related to the value 1000, as the umlaut
> is used to mark the second derivative.
> (page 28-29 or slide 41-42)

Kind of an odd usage, since ALEF SYMBOL is usually used for transfinite 
cardinals, as in ℵ₀, and you don't normally take time-derivatives of 
those.  But mathematicians love using weird symbols for whatever they 
like.  This is the mathematical usage of two-dots-above, as you note.


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