I am confused by the notation comma.

I know that the comma means 'AND' in Set theory as gate ($a \land b=a$ AND $b$),

But we write solution of equation as $x=1$, $2$ (the equation: $x^2-3x+2=0$)

The question is whether $x=1,2$ is WRONG?

$x=1,2$ $\iff$ $x=1$ AND $x=2$, so rewritten as $x=1$ or $x=2$.

But in so many books, it is written as $x=1$, $2$.

I am confused.....

(PS. I think the comma of $x=1$, $2$ is only notation of classification...? Is it ok?)

  • 3
    $\begingroup$ In this case, the comma is used to separate items as a list. It is a casual, shorthand way of saying "the solutions to $x^2-3x+2=0$ are $x=1$ and $x=2$." We must be careful, though, as $x=1,2$ could be read as $x=1.2$ in the European style. $\endgroup$
    – Emily
    May 2 '14 at 16:55
  • $\begingroup$ Is ',' really AND in set theory? $A:=\{1,2\}$ is the set having $1$ and $2$ as elements, but $x\in A$ is equivalent to $x=1$ or $x=2$. $\endgroup$ May 2 '14 at 17:01
  • $\begingroup$ um.... i mean that 'AND' is a gate($a$^$b=a$ AND $b$) $\endgroup$
    – LeeDH
    May 2 '14 at 17:02
  • $\begingroup$ @LeeDH If you want to keep it simmple, you can write $x=1 \vee x=2$ $\endgroup$ May 2 '14 at 17:47
  • 1
    $\begingroup$ In case writing things symbolically confuses you (or your readers), why not write them out in words? $\endgroup$
    – GEdgar
    May 5 '15 at 12:14

First of all you should know, that there are more countries where the comma is a decimal separator than there are point-separator-countries. (For example: I live in Austria in Europe, and we use the comma as decimal separator.) The international standard since about 100 years is to use a point as decimal separator (before that time the comma was the international decimal separator).

enter image description here

blue: decimal separator is a point ($\pi = 3.14$)
green: decimal separator is a comma ($\pi = 3$,$14$)
red: decimal separator is a momayyez ($\pi = 3٫14$)
other colors: two or all three of the above standards are in use

In Countries where the comma is not used as decimal separator (not-green countries in the picture), it is used as list-separator, for example when you want to list the elements of a set. This is also used internationally:

set = {Apple, Zwetschke, 42, -47.6, 小数点}

In countries where the decimal-separator is a comma (green countries), the semicolon is used als list-separator:

set = {Apple; Zwetschke; 42; -47,6; 小数点}

Often a mathematical problem has more than one solutions (for example $x^2-5x+6$). So the solution is a set of numbers:

Solution = {$x=2$, $x=3$}

But a shorter way to write the same fact is this:

$x = 1, 2$ in point-countries
$x = 1; 2$ in comma-countries


saying x = 1 and x = 2 can be misleading as x can't be both at the same time. So, IMO, don't use the comma as it might be interpreted as AND.

x^2-3x+2 = 0

x=1 or x=2

i.e one or the other but not both at the same time

It's not a lot to ask given that it immediately avoids any miscommunication


Sometimes comma is used as 'OR'. And, surprisingly as it might seem, we use commas as punctuation=)

Moreover, in some countries (Russia, for example), comma is also used as decimal separator. For me, in particular, the line $x=1,\!2$ looks equivalent to $x=6/5$ and not to $x_1=1,\,x_2=2$.


As far as I know,

$$ x = 1, 2 $$

is rather unconventional, but most people will still understand what you mean. So it is not necessarily wrong, but it is admittedly somewhat confusing, since it appears to claim that $ x $ equals two distinct values simultaneously, which of course is impossible.

Either of these are clearer:

$$ x \in \{1, 2\} $$ $$ x = 1.5 \pm 0.5 $$


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