|
â„
In set theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers \mathbb R, sometimes called the continuum. It is an infinite cardinal number and is denoted by \mathfrak c (lowercase fraktur "c") or , \mathbb R, . The real numbers \mathbb R are more numerous than the natural numbers \mathbb N. Moreover, \mathbb R has the same number of elements as the power set of \mathbb N. Symbolically, if the cardinality of \mathbb N is denoted as \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'' \mathfrak c . Alternative explanation for 𝔠 = 2ℵ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fraktur
Fraktur () is a calligraphic hand of the Latin alphabet and any of several blackletter typefaces derived from this hand. The blackletter lines are broken up; that is, their forms contain many angles when compared to the curves of the Antiqua (common) typefaces modeled after antique Roman square capitals and Carolingian minuscule. From this, Fraktur is sometimes contrasted with the "Latin alphabet" in northern European texts, which is sometimes called the "German alphabet", simply being a typeface of the Latin alphabet. Similarly, the term "Fraktur" or "Gothic" is sometimes applied to ''all'' of the blackletter typefaces (known in German as , "Broken Script"). The word derives from Latin ("a break"), built from , passive participle of ("to break"), the same root as the English word "fracture". Characteristics Besides the 26 letters of the ISO basic Latin alphabet, Fraktur includes the ( ), vowels with umlauts, and the (''long s''). Some Fraktur typefaces also include a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
