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We know that in writings in mathematics, variables are usually italicised. Now the question is, in handwriting on the board, how should we write the variables differently?

As an example, say I want to write the following:

The following statement is true for all real number $x$: $$\sin^2 x+\cos^2 x=1.$$

Here are some possibilities:

  1. Write the variable $x$ as x without any changes in the font.
  2. Purposefully write $x$ using a "handwritten italic" font.
  3. Write $x$ as x but with a different colour.

Is there any preferred/suggested practice on this?

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  • $\begingroup$ A nice related question: matheducators.stackexchange.com/q/41/5153 $\endgroup$ – pjs36 Feb 8 '18 at 22:08
  • $\begingroup$ In Russian all letters are handwritten in cursive rather than in block (printed) form, so in particular the Cyrillic letter x is always handwritten as $x$. Being forced to write x as $x$ when studying Russian had an immediate potential effect on my math handwriting. Consider finding a local Russian speaker and ask that person how to smoothly write a cursive Russian x in one stroke (without having to lift your pen off the paper). $\endgroup$ – KCd Feb 15 '18 at 13:09
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I choose (1). On the board, write an x normally. There is no distinction between roman and italic in this setting.

Back in the Olden Days (before personal computers) I would accosionally need to denote italic in a special way. In instructions to a typesetter where my manuscript would be prepared for printing I would denote italic x in a special way (conventionally an underline).

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  • $\begingroup$ Thanks for your answer! Is there any reason why Choice (2) is not practised? $\endgroup$ – Zuriel Feb 8 '18 at 16:44
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    $\begingroup$ Yes. It's more work and not needed. Just do choice one and don't use x for cross multiply. Somehow we got through decades of math instruction without this being a problem! $\endgroup$ – guest Feb 8 '18 at 19:26
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My preferred choice is (2), which is also probably the most used in my country.

You can use (1) if you don't have to perform numerical calculations too, for otherwise the x can be confused with the multiplication cross (and avoid the dot for the multiplication symbol between numbers, because on the blackboard is barely readable).

And I'd avoid (3) because frequent colour switches disrupt the writing flow.

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  • $\begingroup$ Seems amazing to me! Let's understand this better. When you write $\mathrm{Ext}\; G$ you use a different letter x than when you write $x + 2$ ... ??? And how about (in continental Europe, where they write $\int f(x)\;\mathrm{d}x$ with roman d and italic x) ... would you still do that on the board? $\endgroup$ – Gerald Edgar Feb 8 '18 at 19:33
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    $\begingroup$ @GeraldEdgar Yes, exactly. For what concerns the integral sign, it's not that all continental Europe writes $\int f(x)\;\mathrm{d}x$, as not all the English-speaking world writes $\int f(x)\;d x$, but, yes, I try to write the former too (even though with my poor handwriting skills the distinction might not be so clear). $\endgroup$ – Massimo Ortolano Feb 8 '18 at 19:41
  • $\begingroup$ @GeraldEdgar As a curiosity, I once tried to write the mathematical $x$ as a normal x: I wasn't able to do this consistently because I learnt to write them differently when I was a child. $\endgroup$ – Massimo Ortolano Feb 8 '18 at 19:57
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One letter probably causes more confusion than all the others put together: x, because of its similarity to $\times$ (multiplication as taught in schools). What I was taught in the UK (20 years ago) and still use routinely is (with LaTeX equivalents) as follows:

x, times, and X

This is also how I write x in normal handwriting, but that's by no means universal. The capital is noticeably taller than $\times$ when written on the same line.

I believe, from what I've seen in a university physics department, that this approach is still very common (among students and academics of all ages). We tend to use $\times$ for multiplication more than mathematicians, but even if you use $\cdot$ there's always the cross product of vectors to consider.

This is close to your option 2, but (i) specific to x, and (ii) not really italic, just different.

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    $\begingroup$ I would only use $\times$ for the cross product, which would then require the variables on either side to be indicated as vectors (usually via arrows). I distinguish capital X from lowercase by adding serifs to the former. $\endgroup$ – aeismail Feb 12 '18 at 21:43
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If the increased clarity of "math mode" is worth it in print, I don't see why it wouldn't be worth it on the board. So I'm on choice (2); my current whiteboard font has a "math mode" $f, x, y$ that look different from normal f, x, y. I'm rendering the sentence

$y = f(x)$ is foxy.

as approximately

enter image description here

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Surely mathematicians would just use the triple bar identity symbol, and it doesn't have to be defined. I was introduced to it in later grade school (O-levels). Special notations are not conducive to the proper training of students in standard notations perfectly acceptable in exams.

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