Inequality symbols

Inequality symbols are symbols that are used to indicate inequality relations. Together with other mathematical symbols such as the equals sign (=), which indicates an equality relation, they are sometimes referred to as relation symbols.

Strict inequalities include less than (<) and greater than (>) symbols, described below. Although an equals sign is not technically an inequality symbol, it is discussed together with inequality symbols since it is included as part of non-strict inequalities such as greater than or equal to (≥) and less than or equal to (≤).

Equals sign: =

The equals sign, symbolized as "=" indicates equality. Expressions on either side of an equals sign either have the same value, or have the same value for certain values. Equality (as well as inequality) is a basis for solving algebraic equations and inequalities.

2 = 2

5 + 3 = 1 + 7

x = x

All of the above equations are true. In cases where the values are not equal, we can use a number of different inequality symbols, such as the not equal to sign.

Not equal to sign: ≠

The not equal to sign, also referred to as the does not equal sign, is a symbol that indicates the inequality of the values or expressions on either side of the symbol.

12 ≠ 17

x2 ≠ x3

x - 7 ≠ x + 7

While the above use of ≠ is true for all the cases, it doesn't tell us much other than that the expressions on either side of the symbol are not equal. There are other, more specific inequality relations, like those below.

Greater than sign: >

The greater than sign is a symbol that indicates a strict inequality between two values; specifically, that the value to the left of the greater than sign is larger than the value on the right. Greater than is a strict inequality, meaning that the value on the left of the sign must be greater than the value on the right; they cannot be equal. The following are valid uses of the greater than sign:

5 > 4

x2 > x

x + 12 > x + 7

Generally, given

a > b

a must be greater than b. Thus, if b were 4, a could be any value above 4, but not 4. In cases where a can also equal 4, we would use the greater than or equal to sign instead.

Greater than or equal to sign: ≥

The greater than or equal to sign is a symbol that indicates that the value on the left hand side of the symbol is either greater than, or equal to the value on the right. This can also be read as the value on the left hand side is at least equal to the value on the right. Given

a ≥ b

a can equal b, unlike the greater than sign. This is because ≥ does not denote a strict inequality. This is the only difference between ">" and "≥".

Less than sign: <

The less than sign is the counterpart to the greater than sign. It indicates a strict inequality between two values; specifically, the value on the left of the less than sign is smaller than the value on the right. The following are valid uses of the less than sign:

3 < 5

x2 < x4

x - 12 < x - 4

Generally, given

a < b

the value of a must be less than that of b. They cannot be equal. If we want to denote that a can be less than or equal to b, we would use the less than or equal to sign (≤) instead.

Less than or equal to sign: ≤

The less than or equal to sign is a symbol that indicates that the value on the left hand side of the symbol is either less than, or equal to the value on the right. This can also be read as meaning that the value or expression on the left hand side of the symbol can at most be equal to the value on the right, never greater. Generally, given

a ≤ b

a can be equal to b. Unlike the less than sign, ≤ does not denote a strict inequality. This is the only difference between "<" and "≤".