U+1D520 Mathematical Fraktur Small C
U+1D520 was added to Unicode in version 3.1 (2001). It belongs to the block
This character is a Lowercase Letter and is commonly used, that is, in no specific script.
The glyph is a Font composition of the glyph
The Wikipedia has the following information about this codepoint:
In set theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers R {displaystyle mathbb {R} } , sometimes called the continuum. It is an infinite cardinal number and is denoted by c {displaystyle {mathfrak {c}}} (lowercase Fraktur "c") or | R | {displaystyle |mathbb {R} |} .
The real numbers R {displaystyle mathbb {R} } are more numerous than the natural numbers N {displaystyle mathbb {N} } . Moreover, R {displaystyle mathbb {R} } has the same number of elements as the power set of N . {displaystyle mathbb {N} .} Symbolically, if the cardinality of N {displaystyle mathbb {N} } is denoted as ℵ 0 {displaystyle aleph _{0}} , the cardinality of the continuum is
This was proven by Georg Cantor in his uncountability proof of 1874, part of his groundbreaking study of different infinities. The inequality was later stated more simply in his diagonal argument in 1891. Cantor defined cardinality in terms of bijective functions: two sets have the same cardinality if, and only if, there exists a bijective function between them.
Between any two real numbers a < b, no matter how close they are to each other, there are always infinitely many other real numbers, and Cantor showed that they are as many as those contained in the whole set of real numbers. In other words, the open interval (a,b) is equinumerous with R . {displaystyle mathbb {R} .} This is also true for several other infinite sets, such as any n-dimensional Euclidean space R n {displaystyle mathbb {R} ^{n}} (see space filling curve). That is,
The smallest infinite cardinal number is ℵ 0 {displaystyle aleph _{0}} (aleph-null). The second smallest is ℵ 1 {displaystyle aleph _{1}} (aleph-one). The continuum hypothesis, which asserts that there are no sets whose cardinality is strictly between ℵ 0 {displaystyle aleph _{0}} and c {displaystyle {mathfrak {c}}} , means that c = ℵ 1 {displaystyle {mathfrak {c}}=aleph _{1}} . The truth or falsity of this hypothesis is undecidable and cannot be proven within the widely used Zermelo–Fraenkel set theory with axiom of choice (ZFC).
Representations
System | Representation |
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Nº | 120096 |
UTF-8 | F0 9D 94 A0 |
UTF-16 | D8 35 DD 20 |
UTF-32 | 00 01 D5 20 |
URL-Quoted | %F0%9D%94%A0 |
HTML hex reference | 𝔠 |
Wrong windows-1252 Mojibake | ð” |
HTML named entity | 𝔠 |
LATEX | \mathfrak{c} |
Related Characters
Confusables
Elsewhere
Complete Record
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3.1 (2001) | |
MATHEMATICAL FRAKTUR SMALL C | |
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