alephn.

Brit.

/ˈalɛf/,

/ˈɑːlɛf/,

/ˈalɪf/,

/ˈɑːlɪf/, U.S.

/ˈɑlɛf/,

/ˈɑləf/

Forms: Middle English allef, Middle English– aleph, 1500s–1600s alephe, 1800s– alef (in sense 2). Also with capital initial.

Origin: Of multiple origins. Partly a borrowing from Latin. Partly a borrowing from Hebrew. Etymons: Latin aleph; Hebrew 'ālep̄.

Etymology: < (i) post-classical Latin aleph (4th cent.), and its etymon (ii) Hebrew 'ālep̄ < Phoenician 'lp (probably ālep̄ ), lit. ‘ox’, the letter being so called on account of its original resemblance to the head of an ox (compare quot. 2003 at sense 1). Compare Middle French, French aleph (c1400; rare before 1751), Spanish aleph (c1300), Italian aleph (a1322 as †alep , c1400 as †alef ). Compare earlier alpha n.In aleph null n., aleph-zero n. at Compounds after German Alef-null (G. Cantor 1895, in Math. Ann. 46 492; Cantor introduced the symbol for aleph-null slightly earlier in the same paper, on page 488).

1. The name of the first letter of the Hebrew, Phoenician, and other north Semitic alphabets, in printed square Hebrew having the form א. Cf. alif n., alpha n.In north Semitic alphabetic writing, the letter aleph represents the glottal stop. In post-biblical Hebrew, it is used in certain contexts to represent the number 1.

ΘΚΠ

society > communication > writing > written character > name of written character > [noun] > Semitic

alephc1300

vau1382

yod1534

waw1832

vav1869

c1300 Childhood Jesus (Laud) 800 in C. Horstmann Altengl. Legenden (1875) 1st Ser. 28 Ȝwi was Allef furst bi founde? Of alle lettres he is þe furste.

?a1425 Mandeville's Trav. (Egerton) (1889) 54 What kyn lettres þe Iews usez..and þe names of þe lettres also, as þai call þam:—Aleph [etc.].

1547 J. Hooper Answer Detection Deuyls Sophistrye sig. O2^v Euery lew..beginnith to teach his child the 20. chapiter of Exod. as sonne as he can speke Aleph.

1596 H. Broughton Daniel ix. sig. I4^v In the Greeke prouerbiall speech Α and Ω after the Ebrews, from Aleph vnto Thau.

1664 T. Herbert Some Years Trav. (new ed.) 131 The first verse of the first chapter of Genesis where the letter Aleph is six times found.

1701 N. Grew Cosmol. Sacra iv. i. 142 The Hebrews, did use three of their Letters, called Matres Lectionis, viz. Aleph, Vau, and Jod, instead of Vowels.

1772 C. Davy Conjectural Observ. Alphabetic Writing 66 The figure of א, i. e. aleph or alpha,..gave an idea of the ox to the inhabitants of the Eastern coasts of the Mediterranean.

?1820 S. T. Coleridge Coll. Lett. (1971) V. 99 The Aleph, say the Rabbinical Philologists, is no Letter; but that in and with which all Letters are or become.

1875 Encycl. Brit. I. 608/2 The Phoenician alphabet consisted of twenty-eight letters, which for convenience we may call by the names of their Hebrew equivalents. These were (1) Aleph (2) Beth, (3) Gimel, [etc.].

1930 E. A. W. Budge Amulets & Superstitions (1978) viii. 234 In this case the initial letter or ‘key’ is the aleph in the middle of the third line.

1976 J. F. A. Sawyer Mod. Introd. Biblical Hebrew 8 Aleph not pronounced, except between vowels where it stands for a glottal stop.

2003 D. Sacks Let. Perfect 51 Two horns are still evident in the Phoenician aleph of 1000 B.C.

2. Mathematics. Each of a class of transfinite numbers representing the cardinality of infinite sets; an infinite cardinal number. Symbol ℵ.First recorded in aleph-zero n. at Compounds.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > [noun] > infinity > transfinite number

aleph1899

1899 Math. Gaz. 1 304 The smallest transfinite number, viz. that which corresponds to the assemblage of all integers, is symbolized by ℵ₀ (alef-zero), and it is shown that any integral algebraical expression as ℵ₀ with finite coefficients and indices is equal to ℵ₀.

1920 A. S. Eddington Space, Time & Gravitation iii. 59 It reminds us of the mathematicians' transfinite number Aleph; you can subtract any number you like from it and it still remains the same.

1923 Amer. Jrnl. Math. 45 87 The non-existence of certain cardinals which are not Alephs.

1963 B. S. Johnson Travelling People i. 19 It would be a noble achievement to find the square root of aleph one.

1989 Math. Teacher 82 291/2 A generalized continuum hypothesis assumes that the sequence of alephs are the only transfinite numbers.

2004 M. Potter Set Theory & its Philos. xv. 261 An infinite well-orderable cardinal is called an aleph.

Compounds

aleph null n. Mathematics the smallest infinite cardinal number; the number of positive integers (1, 2, 3,… ).

ΚΠ

1903 Proc. London Math. Soc. 14 May 243 Cantor uses the notation ℵ₁ or Aleph-eins for the potency of his numbers of the first potency, while ℵ₀ or Aleph-null denotes the potency of a countable set of points; this notation we shall keep.

1979 Sci. Amer. Nov. 29/2 There is no infinite number between aleph-null (the number of positive integers) and aleph-one (the number of real numbers).

2007 W. Byers How Mathematicians Think iv. 163 Countable infinity is the cardinality of the counting numbers. It is usually represented by the symbol ℵ₀, aleph null.

aleph-zero n. Mathematics = aleph null n.

ΚΠ

1899 [see sense 2].

1954 Jrnl. Symbolic Logic 19 257 It is no longer possible to prove the existence of any cardinal number greater than aleph-zero (the number of positive integers) in ∑_ω.

2002 J. A. Benardete in D. Jacquette Compan. Philos. Logic xxiii. 352 Let all of space time be packed solid with dogs cheek by jowl: that will yield no more than aleph-zero of them.

This entry has been updated (OED Third Edition, September 2012; most recently modified version published online December 2021).

单词	aleph
释义	alephn. Brit. /ˈalɛf/, /ˈɑːlɛf/, /ˈalɪf/, /ˈɑːlɪf/, U.S. /ˈɑlɛf/, /ˈɑləf/ Forms: Middle English allef, Middle English– aleph, 1500s–1600s alephe, 1800s– alef (in sense 2). Also with capital initial. Origin: Of multiple origins. Partly a borrowing from Latin. Partly a borrowing from Hebrew. Etymons: Latin aleph; Hebrew 'ālep̄. Etymology: < (i) post-classical Latin aleph (4th cent.), and its etymon (ii) Hebrew 'ālep̄ < Phoenician 'lp (probably ālep̄ ), lit. ‘ox’, the letter being so called on account of its original resemblance to the head of an ox (compare quot. 2003 at sense 1). Compare Middle French, French aleph (c1400; rare before 1751), Spanish aleph (c1300), Italian aleph (a1322 as †alep , c1400 as †alef ). Compare earlier alpha n.In aleph null n., aleph-zero n. at Compounds after German Alef-null (G. Cantor 1895, in Math. Ann. 46 492; Cantor introduced the symbol for aleph-null slightly earlier in the same paper, on page 488). 1. The name of the first letter of the Hebrew, Phoenician, and other north Semitic alphabets, in printed square Hebrew having the form א. Cf. alif n., alpha n.In north Semitic alphabetic writing, the letter aleph represents the glottal stop. In post-biblical Hebrew, it is used in certain contexts to represent the number 1. ΘΚΠ society > communication > writing > written character > name of written character > [noun] > Semitic alephc1300 vau1382 yod1534 waw1832 vav1869 c1300 Childhood Jesus (Laud) 800 in C. Horstmann Altengl. Legenden (1875) 1st Ser. 28 Ȝwi was Allef furst bi founde? Of alle lettres he is þe furste. ?a1425 Mandeville's Trav. (Egerton) (1889) 54 What kyn lettres þe Iews usez..and þe names of þe lettres also, as þai call þam:—Aleph [etc.]. 1547 J. Hooper Answer Detection Deuyls Sophistrye sig. O2^v Euery lew..beginnith to teach his child the 20. chapiter of Exod. as sonne as he can speke Aleph. 1596 H. Broughton Daniel ix. sig. I4^v In the Greeke prouerbiall speech Α and Ω after the Ebrews, from Aleph vnto Thau. 1664 T. Herbert Some Years Trav. (new ed.) 131 The first verse of the first chapter of Genesis where the letter Aleph is six times found. 1701 N. Grew Cosmol. Sacra iv. i. 142 The Hebrews, did use three of their Letters, called Matres Lectionis, viz. Aleph, Vau, and Jod, instead of Vowels. 1772 C. Davy Conjectural Observ. Alphabetic Writing 66 The figure of א, i. e. aleph or alpha,..gave an idea of the ox to the inhabitants of the Eastern coasts of the Mediterranean. ?1820 S. T. Coleridge Coll. Lett. (1971) V. 99 The Aleph, say the Rabbinical Philologists, is no Letter; but that in and with which all Letters are or become. 1875 Encycl. Brit. I. 608/2 The Phoenician alphabet consisted of twenty-eight letters, which for convenience we may call by the names of their Hebrew equivalents. These were (1) Aleph (2) Beth, (3) Gimel, [etc.]. 1930 E. A. W. Budge Amulets & Superstitions (1978) viii. 234 In this case the initial letter or ‘key’ is the aleph in the middle of the third line. 1976 J. F. A. Sawyer Mod. Introd. Biblical Hebrew 8 Aleph not pronounced, except between vowels where it stands for a glottal stop. 2003 D. Sacks Let. Perfect 51 Two horns are still evident in the Phoenician aleph of 1000 B.C. 2. Mathematics. Each of a class of transfinite numbers representing the cardinality of infinite sets; an infinite cardinal number. Symbol ℵ.First recorded in aleph-zero n. at Compounds. ΘΚΠ the world > relative properties > number > mathematical number or quantity > [noun] > infinity > transfinite number aleph1899 1899 Math. Gaz. 1 304 The smallest transfinite number, viz. that which corresponds to the assemblage of all integers, is symbolized by ℵ₀ (alef-zero), and it is shown that any integral algebraical expression as ℵ₀ with finite coefficients and indices is equal to ℵ₀. 1920 A. S. Eddington Space, Time & Gravitation iii. 59 It reminds us of the mathematicians' transfinite number Aleph; you can subtract any number you like from it and it still remains the same. 1923 Amer. Jrnl. Math. 45 87 The non-existence of certain cardinals which are not Alephs. 1963 B. S. Johnson Travelling People i. 19 It would be a noble achievement to find the square root of aleph one. 1989 Math. Teacher 82 291/2 A generalized continuum hypothesis assumes that the sequence of alephs are the only transfinite numbers. 2004 M. Potter Set Theory & its Philos. xv. 261 An infinite well-orderable cardinal is called an aleph. Compounds aleph null n. Mathematics the smallest infinite cardinal number; the number of positive integers (1, 2, 3,… ). ΚΠ 1903 Proc. London Math. Soc. 14 May 243 Cantor uses the notation ℵ₁ or Aleph-eins for the potency of his numbers of the first potency, while ℵ₀ or Aleph-null denotes the potency of a countable set of points; this notation we shall keep. 1979 Sci. Amer. Nov. 29/2 There is no infinite number between aleph-null (the number of positive integers) and aleph-one (the number of real numbers). 2007 W. Byers How Mathematicians Think iv. 163 Countable infinity is the cardinality of the counting numbers. It is usually represented by the symbol ℵ₀, aleph null. aleph-zero n. Mathematics = aleph null n. ΚΠ 1899 [see sense 2]. 1954 Jrnl. Symbolic Logic 19 257 It is no longer possible to prove the existence of any cardinal number greater than aleph-zero (the number of positive integers) in ∑_ω. 2002 J. A. Benardete in D. Jacquette Compan. Philos. Logic xxiii. 352 Let all of space time be packed solid with dogs cheek by jowl: that will yield no more than aleph-zero of them. This entry has been updated (OED Third Edition, September 2012; most recently modified version published online December 2021). < n.c1300
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