TITLE: How do you distinguish the difference between a negative sign and a minus sign in Algebra
QUESTION [8 upvotes]: Both the negative sign symbol and subtraction's minus symbol look the same, so how does anyone tell them apart?

REPLY [3 votes]: I beg to differ with the wikipedia description, which seems to be written for the feeble of mind, but does not describe the use of the sign "$-$" in mathematics, or in computer programming, correctly. Notably there is no need at all to distinguish the use of a "negative indicator" (case 2., as in $-5$) from the use as a (unary) "negation operator" (case 3. ,as in $-x$, or I suppose for instance in $-\pi$ or in $-i$ when $i$ designates the imaginary unit). One can of course decree that case 2. applies if and only if the sign "$-$" has no left operand and a right operand that is an explicit numeric constant (a sequence of digits, possible fractional part starting with  decimal point); one then needs to remove that case from case 3. to avoid ambiguity. But the point is that case 3. perfectly well covers cases like $-5$ or $-5.272023$: the value denoted is the opposite of that of the (right) operand of the minus sign. Saying that case 2. is a "negative sign" has no added value; it just happens that explicit numeric constants as described above always designate non-negative numbers, so that particular case always describes a non-positive real number. Making the distinction just raises useless questions like whether there is a negative indicator in $-\frac15$, and in $-1/5$? Or in $-0.00$, which is no more negative than $0$ is positive. Therefore I would say

There is no such thing as a negative sign in mathematics. To expresss the fact that the value of an expression $E$ is negative, one writes $E<0$, and this does not involve the sign "$-$" at all.
The basic meaning of "$-$" is as a binary operator, where $x-y$ describes the unique value $z$ such that $z+y=x$.
When used without a left operand (so as a unary operator) the value $0$ is implicitly taken as left operand. So $-x$ means $0-x$. And $-5$ means $0-5$, the unique value $z$ such that $z+5=0$, which might seem roundabout, but is correct.

The fact that $-5$ is not an explicit constant expression like $24$, but the resultof applying a unary operator to "$5$", and that the value denoted by "$-5$" does not have any direct numeric representation should not be shocking; neither do $\pi$  or $\frac17$ (because decimals have to stop somewhere) or $3+4i$ have any numeric constant designating them, without using operators. As far as programming goes, I hardly know any language whose syntax for numeric constants allows for $-5$; most if not all would take that to be the unary minus applied to the constant $5$. (However if scientific notation with exponent-of-$10$ is included, the possible minus sign for the exponent will be part of the constant syntax, as an operator makes no sense in that position.)
So the only relevant question is whether "$-$" is used in a specific case as unary or binary operator, which is determined merely by the absence or presence of an applicable left operand; which is the case is quite clear in practice.
I might add that it makes sense in the points above to reverse the order in discussing unary and binary use, making $-x$ the more basic case (the unique value $z$ with $z+x=0$), and considering $x-y$ and abbreviation for $x+-y$; in the end for the meaning of each operator it makes no difference which approach is used.