Signs used in algebra

In algebra, the signs plus (+) and minus (-) have their ordinary meaning, indicating addition and subtraction and also serve to distinguish¹ between opposite kinds of numbers, positive (+) and negative (-). In such an operation as +10-10=0, the minus sign means that the minus 10 is combined with the plus 10 to give a zero result² or that 10 is subtracted from 10 to give a zero remainder.

The so-called “double sign” (±), which is read “plus-or-minus”, is sometimes used. It means that the number or symbol which it precedes may be “either plus or minus”³ or “both plus and minus”⁴.

As in arithmetic, the equality sign (=) means “equals” or “is equal to”.

The multiplication sign (×) has the same meaning as in arithmetic. In many cases, however, it is omitted. A dot (·) placed between any two numbers a little above the line (to distinguish it from a decimal point) is sometimes used as a sign of multiplication.

The division sign (÷) has the same meaning as in arithmetic. It is frequently replaced by the fraction line; thus 6/3 means the same as 6÷3 and in both cases the result or quotient is 2. The two dots above and below the line in the division sign (÷) indicate the position of the numerator and denominator in a fraction, or the dividend and divisor in division.

Parentheses (), brackets [ ], braces { }, and other inclosing signs are used to indicate that everything between the two signs is to be treated as⁵ a single quantity and any sign placed before it refers to everything inside as a whole and to every part of the complete expression inside.

Another sign which is sometimes useful is the sign which means “greater than” or “less than”. The sign (>) means “greater than” and the sign (<) means “less than”. Thus, a>b means that “a is greater than b”, and 3<5 means “3 is less than 5”.

The sign.·., three dots at the corners of a triangle, means “hence” or “therefore”.

Notes:

¹ serve to distinguish – служат для того, чтобы различить

² to give a zero result – дать в результате нуль

³ either plus and minus – либо плюс, либо минус

⁴ both plus and minus – как плюс, так и минус

⁵ is to be treated as – следует рассматривать как