Built-in Mathematica Symbol

Unequal (, ≠)

lhs

rhs or lhs≠rhs
returns False if lhs and rhs are identical.

MORE INFORMATION

can be entered as x\[NotEqual]y or Esc Esc .

lhs≠rhs returns True if lhs and rhs are determined to be unequal by comparisons between numbers or other raw data, such as strings.

Approximate numbers are considered unequal if they differ beyond their last two decimal digits.

gives True only if none of the e_i are equal. 2≠3≠2False.

lhs≠rhs represents a symbolic condition that can be generated and manipulated by functions like Reduce and LogicalExpand.

Unequal[e] gives True.

For exact numeric quantities, Unequal internally uses numerical approximations to establish inequality. This process can be affected by the setting of the global variable $MaxExtraPrecision.

In StandardForm, Unequal is printed using ≠.

EXAMPLES

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Basic Examples (2)

Returns True if elements are guaranteed unequal, and otherwise stays unevaluated:

Enter as

or as Esc

Esc:

Returns True if elements are guaranteed unequal, and otherwise stays unevaluated:

In[1]:=

Out[1]=

Enter as

or as Esc

Esc:

In[1]:=

Out[1]=

Scope (11)

Test unequality of numbers:

Approximate numbers that differ in at most their last eight binary digits are considered equal:

Compare an exact numeric expression and an approximate number:

Compare two exact numeric expressions; a numeric test may suffice to prove unequality:

Proving equality requires symbolic methods:

Symbolic methods used by Unequal are insufficient to prove this False:

Use RootReduce to decide whether two algebraic numbers are unequal:

Numeric methods used by Unequal do not use sufficient precision to prove this unequality:

RootReduce proves that the two algebraic numbers are not equal:

Increasing $MaxExtraPrecision may also prove unequality:

This symbolic unequality is always False:

Unequal does not automatically prove this unequality:

Use Expand to prove it:

Compare more than two expressions:

Compare lists:

Compare strings:

Properties & Relations (4)

The negation of two-argument Unequal is Equal:

The negation of three-argument Unequal does not simplify automatically:

Use LogicalExpand to express it in terms of two-argument Equal:

The negation of three-argument Unequal is not equivalent to three-argument Equal:

Unequal tests mathematical unequality of objects represented by expressions:

UnsameQ tests syntactic unequality of expressions:

When Unequal cannot decide whether two numeric expressions are equal it returns unchanged:

FullSimplify uses exact symbolic transformations to disprove the unequality:

PossibleZeroQ uses numeric and symbolic heuristics to decide whether an expression is zero:

Numeric methods used by PossibleZeroQ may incorrectly decide that a number is zero:

Possible Issues (3)

Unequality for machine-precision approximate numbers can be subtle:

The extra digits disrupt equality:

Arbitrary-precision approximate numbers do not have this problem:

Thanks to automatic-precision tracking Unequal knows to look only at the first ten digits:

In this case, the unequality test for machine numbers gives the expected result:

The extra digits in this case are ignored by Unequal: