NumberQ¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

NumberQ[expr]

gives True if expr is an explicit number (Integer, BigInt, Rational, Real, MPFR, or Complex), and False otherwise. Symbolic constants such as Pi give False; use NumericQ for those.

Examples (15)¶

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (4)¶

In[1]:= StringQ["AbC"]
Out[1]= True

In[2]:= StringQ[""]
Out[2]= True

In[3]:= StringQ[123]
Out[3]= False

In[4]:= StringQ[] StringQ::argx: StringQ called with 0 arguments; 1 argument is expected.

Scope (6)¶

In[5]:= MachineNumberQ[Sin[1000.]]
Out[5]= True

Overflows to +inf

In[6]:= MachineNumberQ[Exp[1000.]]
Out[6]= False

In[7]:= MachineNumberQ[-29037945.290347]
Out[7]= True

MPFR, not machine

In[8]:= MachineNumberQ[N[Pi, 30]]
Out[8]= False

In[9]:= MachineNumberQ[1.0 + 2.0 I]
Out[9]= True

Exact Gaussian integer

In[10]:= MachineNumberQ[1 + 2 I]
Out[10]= False

Applications (5)¶

In[11]:= NumberQ[3]
Out[11]= True

In[12]:= NumberQ[2/3]
Out[12]= True

In[13]:= NumberQ[1 + 2 I]
Out[13]= True

A symbolic constant is not an explicit number

In[14]:= NumberQ[Pi]
Out[14]= False

In[15]:= NumberQ[x]
Out[15]= False

Implementation notes¶

builtin_numberq (src/core.c) returns True for an explicit number — EXPR_INTEGER, EXPR_REAL, EXPR_BIGINT, EXPR_MPFR (under USE_MPFR), or a Rational/Complex head — and False otherwise. (Contrast NumericQ, whose is_numeric_quantity helper also accepts symbolic constants like Pi and numeric-function calls.)

Attributes: Protected.

References¶

See also: AtomQ, IntegerQ, StringQ, MachineNumberQ, Complex, ExactNumberQ

Source: src/core.c
Specification: docs/spec/builtins/expression-information.md
Tests: tests/test_accuracygoal.c
Tests: tests/test_autocompile.c
Tests: tests/test_bigint.c
Tests: tests/test_core.c

Notes & additional examples¶

Notes¶

NumberQ[expr] is True for an explicit number — an integer, bigint, machine or arbitrary-precision real, rational, or complex. It draws the line exactly where NumericQ does not: NumberQ[Pi] is False because Pi is a symbol that merely has a numeric value, whereas NumericQ[Pi] is True. Use NumberQ when you need an already-evaluated literal number, and NumericQ when a symbolic constant or a numeric-function call should also qualify.