# Re: Need help in interpreting symbol 225e (measured by)

From: Philippe Verdy (verdy_p@wanadoo.fr)
Date: Fri Mar 10 2006 - 22:15:15 CST

• Next message: Philippe Verdy: "Re: Need help in interpreting symbol 225e (measured by)"

From: "Keutgen, Walter" <walter.keutgen@be.unisys.com>
> Philippe is right. Because of the very formal mathematical language, it is just dangerous to translate 'measured by' by the common Hungarian verb for measuring. I have searched the web. The only I have found is that in some 'programming language' U+225e is represented by '\measeq'. In some texts the character is called – from the typesetter point of view of course – 'm over equal'. In order to keep the stress on the =, one could opt for 'm equals'. If in other languages one would need another letter, the symbol needs to be added to Unicode, otherwise one ends up with different fonts per language. Or should one then use a glyph variant selector?

In fact in my old curses at university, there was lot ofuse of such augmented equal sign, notably in physics, because it simplifies the reading of equations:

f(x) = f(y)
where f is the name of a projection function of an operator, we just wrote:
x =(f over) y
where f could be any function or operator, possibly with a complex name (such as a function with indices). So this could have been an "m" if this was the name of the projection function. Itcouldhave been a delta as well, andit would closely match (graphically) the other existing Unicode symbol.

A common function used was the average, denoted by a angle operator over the averaged quantity, which would also be a long expression (where the simple use of a very wide circumflex would not be very readable), so instead of writing:
â = ê
we would write:
a =^ e (using the circumflex over the equal sign, and "a" and "e" possibly long expressions)

If the operator was a norm, we would rewrite:
|a| = |b|
as:
a =|| b (with the norm operator denoted over the equal sign)

So it seems to me that U+225E is just a particular precomposed symbol, chosen quite arbitrarily. It is not enough to represent all actual uses, and it may even be very english-centric for a very particular application or some documents produced in some US universities, or discovered in a book or article from a single author (or small group)...

I think that mathematicians and physicians need a more complete set of notations, not reduced to the few ones that are encoded now as precomposed characters. For such notation, Unicode will not help, and it will be easier to use MathML or TeX, that allow more control on the final layout, and better respect of the semantics (lost by the existing precomposed characters as they are not decomposable)

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