| Information | |
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| has gloss | eng: In mathematics, the cardinality of the continuum, sometimes also called the power of the continuum, is the size (cardinality) of the set of real numbers \mathbb R (sometimes called the continuum). The cardinality of \mathbb R is denoted by |\mathbb R| or by the symbol \mathfrak c (a lowercase Fraktur letter C). As a cardinal number, \mathfrakc} is equal to Beth one (\mathfrak c = \beth}_1}). If the continuum hypothesis holds, then \mathfrakc} is also equal to Aleph one (\mathfrak c = \aleph}_1}). |
| lexicalization | eng: cardinality of the continuum |
| lexicalization | eng: ℭ |
| instance of | (noun) the number of elements in a mathematical set; denotes a quantity but not the order cardinal number, cardinal |
| Meaning | |
|---|---|
| Czech | |
| has gloss | ces: Mohutnost kontinua je matematický pojem z oblasti teorie množin. |
| lexicalization | ces: Mohutnost kontinua |
| French | |
| has gloss | fra: En mathématiques, on dit dun ensemble quil a la puissance du continu, ou parfois le cardinal du continu, sil est équipotent à lensemble des nombres réels, cest-à-dire sil existe une bijection de cet ensemble dans \mathbb R. On montre que lensemble des parties de lensemble des entiers naturels a la puissance du continu, et le cardinal de cet ensemble, et donc de lensemble des réels, est noté 2^\aleph_0}} (où \aleph_0 désigne le cardinal de lensemble des entiers naturels, et donc celui de n'importe quel ensemble dénombrable). |
| lexicalization | fra: puissance du continu |
| Hebrew | |
| has gloss | heb: עוצמת הרצף היא העוצמה של המספרים הממשיים. עוצמת הרצף מסומנת באות \!\ \aleph, וכן מקובל גם הסימון \!\, c לעוצמה זו. |
| lexicalization | heb: עוצמת הרצף |
| Italian | |
| has gloss | ita: In matematica la cardinalità del continuo è il numero cardinale dell'insieme dei numeri reali \mathbfR} (che, a volte, viene chiamato il continuo). Questo numero cardinale viene spesso indicato con il carattere \mathfrak c, :\mathfrak c = |\mathbf R|. |
| lexicalization | ita: Cardinalità del continuo |
| Dutch | |
| has gloss | nld: In wiskunde is de kardinaliteit van het continuüm de grootte (de kardinaliteit) van de verzameling van de reële getallen :\mathbb R (soms aangeduid als het continuüm). De kardinaliteit van \mathbb R wordt vaak aangeduid met \mathfrak c. Per definitie geldt dus dat het kardinaalgetal :\mathfrak c = |\mathbb R |. |
| lexicalization | nld: kardinaliteit van het continuüm |
| Portuguese | |
| has gloss | por: Na matemática, em especial na Teoria dos conjuntos, a cardinalidade do contínuo é a cardinalidade do conjunto dos números reais. Este cardinal costuma ser representado por c: c = |\mathbbR}|\,. |
| lexicalization | por: Cardinalidade do contínuo |
| Swedish | |
| lexicalization | swe: c |
| Chinese | |
| has gloss | zho: 在数学领域, 连续统的势 是实数集 \mathbb R (有时称为连续统)的基数(或势). 集合 \mathbb R 的势记做 |\mathbb R| 或 \mathfrak c (小写歌德体字母 C). 作为基数 \mathfrakc} 等于贝特一(\mathfrak c = \beth}_1}). 如果连续统假设成立, 那么 \mathfrakc} 等于 阿列夫一 (\mathfrak c = \aleph}_1}). |
| lexicalization | zho: 连续统的势 |
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