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# U+230ALeft Floor

U+230A was added in Unicode version 1.1 in 1993. It belongs to the block U+2300 to U+23FF Miscellaneous Technical in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Open Punctuation and is commonly used, that is, in no specific script. The character is also known as APL downstile.

The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is mirrored into Right Floor. U+230A prohibits a line break after it.

In mathematics, the floor function (or greatest integer function) is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted x or floor(x). Similarly, the ceiling function maps x to the smallest integer greater than or equal to x, denoted x or ceil(x).

For example, for floor: ⌊2.4⌋ = 2, ⌊−2.4⌋ = −3, and for ceiling: ⌈2.4⌉ = 3, and ⌈−2.4⌉ = −2.

Historically, the floor of x has been–and still is–called the integral part or integer part of x, often denoted [x] (as well as a variety of other notations). However, the same term, integer part, is also used for truncation towards zero, which differs from the floor function for negative numbers.

For n an integer, n⌋ = ⌈n⌉ = [n] = n.

Although floor(x+1) and ceil(x) produce graphs that appear exactly alike, they are not the same when the value of x is an exact integer. For example, when x=2.0001; ⌊2.0001+1⌋ = ⌈2.0001⌉ = 3. However, if x=2, then ⌊2+1⌋ = 3, while ⌈2⌉ = 2.

## Representations

System Representation
8970
UTF-8 E2 8C 8A
UTF-16 23 0A
UTF-32 00 00 23 0A
URL-Quoted %E2%8C%8A
HTML hex reference &#x230A;
Wrong windows-1252 Mojibake âŒŠ
HTML named entity &LeftFloor;
HTML named entity &lfloor;
alias APL downstile
LATEX \lfloor
digraph 7<

## Complete Record

Property Value
Age (age) 1.1 (1993)
Unicode Name (na) LEFT FLOOR
Unicode 1 Name (na1)
Block (blk) Miscellaneous Technical
General Category (gc) Open Punctuation
Script (sc) Common
Bidirectional Category (bc) Other Neutral
Combining Class (ccc) Not Reordered
Decomposition Type (dt) none
Decomposition Mapping (dm) Left Floor
Lowercase (Lower)
Simple Lowercase Mapping (slc) Left Floor
Lowercase Mapping (lc) Left Floor
Uppercase (Upper)
Simple Uppercase Mapping (suc) Left Floor
Uppercase Mapping (uc) Left Floor
Simple Titlecase Mapping (stc) Left Floor
Titlecase Mapping (tc) Left Floor
Case Folding (cf) Left Floor
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Composition Exclusion (CE)
Case Ignorable (CI)
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)
Cased (Cased)
Full Composition Exclusion (Comp_Ex)
Default Ignorable Code Point (DI)
Dash (Dash)
Deprecated (Dep)
Diacritic (Dia)
Emoji Modifier Base (EBase)
Emoji Component (EComp)
Emoji Modifier (EMod)
Emoji Presentation (EPres)
Emoji (Emoji)
Extender (Ext)
Extended Pictographic (ExtPict)
FC NFKC Closure (FC_NFKC) Left Floor
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hyphen (Hyphen)
ID Continue (IDC)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
IDSU (IDSU) 0
ID_Compat_Math_Continue (ID_Compat_Math_Continue) 0
ID_Compat_Math_Start (ID_Compat_Math_Start) 0
Ideographic (Ideo)
InCB (InCB) None
Indic Mantra Category (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
Jamo Short Name (JSN)
Join Control (Join_C)
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) Left Floor
NFKC Quick Check (NFKC_QC) Yes
NFKC_SCF (NFKC_SCF) Left Floor
NFKD Quick Check (NFKD_QC) Yes
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)
Prepended Concatenation Mark (PCM)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Regional Indicator (RI)
Sentence Break (SB) Close
Soft Dotted (SD)
Sentence Terminal (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)
Bidi Mirrored Glyph (bmg) Right Floor
Bidi Paired Bracket (bpb) Right Floor
Bidi Paired Bracket Type (bpt) Open
East Asian Width (ea) neutral
Hangul Syllable Type (hst) Not Applicable
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Joining Type (jt) Non Joining
Line Break (lb) Open Punctuation
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) Left Floor
Script Extension (scx)
Vertical Orientation (vo) R