Do we have this symbol in mathematics?

Question

It is the symbol I used to show left hand side of inequality isn't greater than right hand side.

More precisely I used this to show the below matrix is not diagonally dominant:

$$\begin{bmatrix}5&6&7\\ 2&-4&2\\ 3&2&-5\\ \end{bmatrix}$$

So at the first row I want to emphasize that $|5|$ is not greater than $|6|+|7|$ therefor instead of writing $|5|<|6|+|7|$ I used the symbol in the image above.

Is it ok to use this symbol in mathematics?

@Randall to show not equal we use $\neq$ so I wrote this to show it is not greater or equal. — Etemon, Dec 17 '20 at 14:59
For a partial ordering, I think it might make sense to speak of $a\not ≥ b$. For a total ordering, as here, why not write $a<b$? — lulu, Dec 17 '20 at 14:59
I know it is the same as $<$ but in this specific problem I want to emphasize left side isn't greater so I used this notation. — Etemon, Dec 17 '20 at 15:00
I think it's fine. When it comes to pedagogy, you're the artist. — littleO, Dec 17 '20 at 15:00
It is common enough that unicode has a code point U+2271 ≱ for that. — achille hui, Dec 17 '20 at 15:03
We could also write $\frac{204}{102}$ for $2$, mathematically correct. But it would not make much sense to use this notation. — Peter, Dec 17 '20 at 15:04
Closed as Opinion-based? Really? Then why we have notation tag on the site if notations are based on opinion? — Etemon, Dec 18 '20 at 00:39

Contestosis · Accepted Answer · 2020-12-17T15:41:44.477

4

To me, it is OK. Putting a bar/cross on a pre-existing maths symbol just means the negation of it.

I'm not sure it is standardized, though.

Edit

As shown by @Dietrich Burde in his answer, these symbols are $\LaTeX$ symbols, so that's clearly OK you can use them.

edited Dec 17 '20 at 15:41

answered Dec 17 '20 at 15:03

Contestosis

1,214

Dietrich Burde · Answer 2 · 2020-12-17T15:18:24.313

3

I would also say that we have both relations $$ x \not\le y, \quad x\not \ge y. $$ There are variants, of course, like $$ x \lneq y,\quad x \gneq y $$ and $$ x\nless y, x\ngtr y $$

edited Dec 17 '20 at 15:18

answered Dec 17 '20 at 15:12

Dietrich Burde

130,978

Just to say: I'd have no guess as to how to interpret $x\lneq y$. To the extent that it means "$x$ is less than but not equal to $y$" then you could just write $x<y$, so I'd imagine that it meant something else...but what? I would not guess that it meant $x>y$. – lulu Dec 17 '20 at 15:25
@lulu The second option has its own LateX command, but it seems just to say that $x<y$ or $x>y$, I agree. Perhaps this is more evident for sets, where $A \subsetneq B$ explicitly says that equality doesn't hold, because $A\subset B$ is ambiguous. – Dietrich Burde Dec 17 '20 at 15:48
Ah, good point. I agree, I wouldn't take $A\subset B$ to exclude $A=B$. – lulu Dec 17 '20 at 15:50

Do we have this symbol in mathematics?

2 Answers2