U+220F N-ARY PRODUCT

U+220F was added to Unicode in version 1.1 (1993). It belongs to the block Mathematical Operators in the Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script. The character is also known as product sign.

The glyph is not a composition. It has a Ambiguous East Asian Width. In bidirectional context it acts as Other Neutral and is not mirrored. The glyph can, under circumstances, be confused with 11 other glyphs. In text U+220F behaves as Ambiguous regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

Multiplication (often denoted by the cross symbol "×", by a point "·" or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division.

The multiplication of two whole numbers is equivalent to adding as many copies of one of them, as the value of the other one:

For example, 3 multiplied by 4 (often said as "3 times 4") can be calculated by adding 3 copies of 4 together:

Here 3 and 4 are the "factors" and 12 is the "product".

One of the main properties of multiplication is the commutative property, adding 3 copies of 4 gives the same result as adding 4 copies of 3:

The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is defined by a systematic generalization of this basic definition.

Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property.

The inverse operation of the multiplication is the division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since the division of a number other than 0 by itself equals 1).

Multiplication is also defined for other types of numbers, such as complex numbers, and more abstract constructs, like matrices. For these more abstract constructs, the order that the operands are multiplied sometimes does matter.

Representations

System Representation
8719
UTF-8 E2 88 8F
UTF-16 22 0F
UTF-32 00 00 22 0F
URL-Quoted %E2%88%8F
HTML-Escape &#x220F;
Wrong windows-1252 Mojibake â
HTML-Escape &prod;
HTML-Escape &Product;
digraph *P
alias product sign
LaTeX \prod
Encoding: EUC-KR (hex bytes) A2 B3
Encoding: MACINTOSH (hex bytes) B8

Complete Record

Property Value
Age (age) 1.1
Unicode Name (na) N-ARY PRODUCT
Unicode 1 Name (na1)
Block (blk) Math_Operators
General Category (gc) Math Symbol
Script (sc) Common
Bidirectional Category (bc) Other Neutral
Combining Class (ccc) Not Reordered
Decomposition Type (dt) None
Decomposition Mapping (dm)
Lowercase (Lower)
Simple Lowercase Mapping (slc)
Lowercase Mapping (lc)
Uppercase (Upper)
Simple Uppercase Mapping (suc)
Uppercase Mapping (uc)
Simple Titlecase Mapping (stc)
Titlecase Mapping (tc)
Case Folding (cf)
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Bidi Paired Bracket (bpb)
Bidi Paired Bracket Type (bpt) None
Cased (Cased)
Composition Exclusion (CE)
Case Ignorable (CI)
Full Composition Exclusion (Comp_Ex)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Dash (Dash)
Deprecated (Dep)
Default Ignorable Code Point (DI)
Diacritic (Dia)
East Asian Width (ea) Ambiguous
Extender (Ext)
FC NFKC Closure (FC_NFKC)
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hangul Syllable Type (hst) Not Applicable
Hyphen (Hyphen)
ID Continue (IDC)
Ideographic (Ideo)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
InMC (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Join Control (Join_C)
Jamo Short Name (JSN)
Joining Type (jt) Non Joining
Line Break (lb) Ambiguous
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) Yes
NFKC Casefold (NFKC_CF)
NFKC Quick Check (NFKC_QC) Yes
NFKD Quick Check (NFKD_QC) Yes
Numeric Type (nt) None
Numeric Value (nv) NaN
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Sentence Break (SB) Other
Simple Case Folding (scf)
Script Extension (scx) Common
Soft Dotted (SD)
STerm (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Other
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)