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# U+2135Alef Symbol

U+2135 was added in Unicode version 1.1 in 1993. It belongs to the block U+2100 to U+214F Letterlike Symbols in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Other Letter and is commonly used, that is, in no specific script. The character is also known as first transfinite cardinal (countable).

The glyph is a compatibility version of the glyph Hebrew Letter Alef. It has no designated width in East Asian texts. In bidirectional text it is written from left to right. When changing direction it is not mirrored. The word that U+2135 forms with similar adjacent characters prevents a line break inside it. The glyph can be confused with one other glyph.

In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Hebrew letter aleph ($\phantom{\rule{thinmathspace}{0ex}}\aleph \phantom{\rule{thinmathspace}{0ex}}$).

The cardinality of the natural numbers is $\phantom{\rule{thinmathspace}{0ex}}{\aleph }_{0}\phantom{\rule{thinmathspace}{0ex}}$ (read aleph-nought or aleph-zero; the term aleph-null is also sometimes used), the next larger cardinality of a well-ordered set is aleph-one $\phantom{\rule{thinmathspace}{0ex}}{\aleph }_{1}\phantom{\rule{thickmathspace}{0ex}},$ then $\phantom{\rule{thinmathspace}{0ex}}{\aleph }_{2}\phantom{\rule{thinmathspace}{0ex}}$ and so on. Continuing in this manner, it is possible to define a cardinal number $\phantom{\rule{thinmathspace}{0ex}}{\aleph }_{\alpha }\phantom{\rule{thinmathspace}{0ex}}$ for every ordinal number $\phantom{\rule{thinmathspace}{0ex}}\alpha \phantom{\rule{thickmathspace}{0ex}},$ as described below.

The concept and notation are due to Georg Cantor, who defined the notion of cardinality and realized that infinite sets can have different cardinalities.

The aleph numbers differ from the infinity ($\phantom{\rule{thinmathspace}{0ex}}\infty \phantom{\rule{thinmathspace}{0ex}}$) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the extended real number line.

## Representations

System Representation
8501
UTF-8 E2 84 B5
UTF-16 21 35
UTF-32 00 00 21 35
URL-Quoted %E2%84%B5
HTML hex reference &#x2135;
Wrong windows-1252 Mojibake â„µ
HTML named entity &alefsym;
HTML named entity &aleph;
alias first transfinite cardinal (countable)
LATEX \aleph

## Complete Record

Property Value
Age (age) 1.1 (1993)
Unicode Name (na) ALEF SYMBOL
Unicode 1 Name (na1) FIRST TRANSFINITE CARDINAL
Block (blk) Letterlike Symbols
General Category (gc) Other Letter
Script (sc) Common
Bidirectional Category (bc) Left To Right
Combining Class (ccc) Not Reordered
Decomposition Type (dt) compatibility
Decomposition Mapping (dm) Hebrew Letter Alef
Lowercase (Lower)
Simple Lowercase Mapping (slc) Alef Symbol
Lowercase Mapping (lc) Alef Symbol
Uppercase (Upper)
Simple Uppercase Mapping (suc) Alef Symbol
Uppercase Mapping (uc) Alef Symbol
Simple Titlecase Mapping (stc) Alef Symbol
Titlecase Mapping (tc) Alef Symbol
Case Folding (cf) Alef Symbol
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) Alef Symbol
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) Hebrew Letter Alef
NFKC Quick Check (NFKC_QC) No
NFKC_SCF (NFKC_SCF) Hebrew Letter Alef
NFKD Quick Check (NFKD_QC) No
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) Other Letter
Soft Dotted (SD)
Sentence Terminal (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Alphabetic Letter
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 Paired Bracket (bpb) Alef Symbol
Bidi Paired Bracket Type (bpt) None
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) Alphabetic
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) Alef Symbol
Script Extension (scx)
Vertical Orientation (vo) U