pointwiseadv.adj.

Brit.

/ˈpɔɪntwʌɪz/, U.S.

/ˈpɔɪntˌwaɪz/

Forms: see point n.¹ and -wise comb. form.

Origin: Formed within English, by compounding. Etymons: point n.¹, -wise comb. form.

Etymology: < point n.¹ + -wise comb. form.

A. adv.

1. In the manner of a point or tip; in respect of points; with the point foremost or uppermost.

ΘΚΠ

the world > space > shape > fact or condition of tapering > condition of tapering to a point > [adverb]

pointwise1545

bodkin-wise1565

acutely1681

pointways1718

spikily1893

1545 Bibliotheca Eliotæ Cuspidatim, poyntyng, or poyntwyse.

1611 J. Florio Queen Anna's New World of Words at Stipula The spindling vp point-wise of any thing namely of corne.

1616 J. Lane Contin. Squire's Tale ix. 197 Gnartolite..whome Akafir, well eienge, point wise smote.

1688 A. Pitfield tr. C. Perrault Mem. Nat. Hist. Animals 238 This Purse, being six Lines at the bottom, at its coming out of the Optick Nerve, and going pointwise towards the top.

1765 tr. A. Goudar Chinese Spy II. lxxx. 257 In China the womens hair grows pointwise: one would think that in France it came out of the head in clusters.

1793 J. Gast Hist. Greece I. viii. 504 Having ordered his right wing to retreat as the other advanced, he bore down on the enemy point-wise, like the beak of a galley.

1904 Westm. Gaz. 25 Feb. 4/1 The bodice..enriched with further appliqués of guipure to extend the fronts pointwise.

1961 New Scientist 21 Dec. 752/3 A ‘diabolo’ has two such triangles in its cross-section (joined pointwise, not edgewise..).

2003 Pittsburgh Post-Gaz. (Nexis) 26 Jan. e11 A pin she had swallowed many months before..had come out of her stomach pointwise.

2. Mathematics. With regard to individual points; esp. (with reference to convergence) with regard to each individual point in a space, but not necessarily for the space as a whole.

ΚΠ

1906 Amer. Jrnl. Math. 28 274 Hence our function can be at most pointwise discontinuous in all three variables together.

1966 A. Feinstein tr. G. Choquet Topol. i. 92 Every sequence (f_n) which converges uniformly to f converges pointwise to f, but it is important to note that the converse is incorrect.

1970 Manifold 6 17 A student produced three new specimens... They came from adding the blackboard examples pointwise.

2004 M. Potter Set Theory & its Philos. 86 If a sequence of continuous functions converges pointwise to a limit function f , then the limit function is also continuous.

B. adj.

Mathematics. Occurring (only) with regard to individual points; esp. (of convergence) occurring with regard to individual points in a space, but not necessarily for the space as a whole.

ΚΠ

1904 Science 18 Nov. 674/2 A proof of some theorems on pointwise discontinuous functions.

1932 Colloquium Publ. Amer. Math. Soc. 15 i. 26 The term ‘convergence in the mean’ was introduced to distinguish convergence in the space ₂..from ordinary point-wise convergence.

1991 C. B. Boyer & U. C. Merzbach Hist. Math. (ed. 2) xviii. 370 He showed that any pointwise construction that can be performed with compasses and straightedge..can be carried out with compasses alone.

This entry has been updated (OED Third Edition, September 2006; most recently modified version published online March 2022).

单词	pointwise
释义	pointwiseadv.adj. Brit. /ˈpɔɪntwʌɪz/, U.S. /ˈpɔɪntˌwaɪz/ Forms: see point n.¹ and -wise comb. form. Origin: Formed within English, by compounding. Etymons: point n.¹, -wise comb. form. Etymology: < point n.¹ + -wise comb. form. A. adv. 1. In the manner of a point or tip; in respect of points; with the point foremost or uppermost. ΘΚΠ the world > space > shape > fact or condition of tapering > condition of tapering to a point > [adverb] pointwise1545 bodkin-wise1565 acutely1681 pointways1718 spikily1893 1545 Bibliotheca Eliotæ Cuspidatim, poyntyng, or poyntwyse. 1611 J. Florio Queen Anna's New World of Words at Stipula The spindling vp point-wise of any thing namely of corne. 1616 J. Lane Contin. Squire's Tale ix. 197 Gnartolite..whome Akafir, well eienge, point wise smote. 1688 A. Pitfield tr. C. Perrault Mem. Nat. Hist. Animals 238 This Purse, being six Lines at the bottom, at its coming out of the Optick Nerve, and going pointwise towards the top. 1765 tr. A. Goudar Chinese Spy II. lxxx. 257 In China the womens hair grows pointwise: one would think that in France it came out of the head in clusters. 1793 J. Gast Hist. Greece I. viii. 504 Having ordered his right wing to retreat as the other advanced, he bore down on the enemy point-wise, like the beak of a galley. 1904 Westm. Gaz. 25 Feb. 4/1 The bodice..enriched with further appliqués of guipure to extend the fronts pointwise. 1961 New Scientist 21 Dec. 752/3 A ‘diabolo’ has two such triangles in its cross-section (joined pointwise, not edgewise..). 2003 Pittsburgh Post-Gaz. (Nexis) 26 Jan. e11 A pin she had swallowed many months before..had come out of her stomach pointwise. 2. Mathematics. With regard to individual points; esp. (with reference to convergence) with regard to each individual point in a space, but not necessarily for the space as a whole. ΚΠ 1906 Amer. Jrnl. Math. 28 274 Hence our function can be at most pointwise discontinuous in all three variables together. 1966 A. Feinstein tr. G. Choquet Topol. i. 92 Every sequence (f_n) which converges uniformly to f converges pointwise to f, but it is important to note that the converse is incorrect. 1970 Manifold 6 17 A student produced three new specimens... They came from adding the blackboard examples pointwise. 2004 M. Potter Set Theory & its Philos. 86 If a sequence of continuous functions converges pointwise to a limit function f , then the limit function is also continuous. B. adj. Mathematics. Occurring (only) with regard to individual points; esp. (of convergence) occurring with regard to individual points in a space, but not necessarily for the space as a whole. ΚΠ 1904 Science 18 Nov. 674/2 A proof of some theorems on pointwise discontinuous functions. 1932 Colloquium Publ. Amer. Math. Soc. 15 i. 26 The term ‘convergence in the mean’ was introduced to distinguish convergence in the space ₂..from ordinary point-wise convergence. 1991 C. B. Boyer & U. C. Merzbach Hist. Math. (ed. 2) xviii. 370 He showed that any pointwise construction that can be performed with compasses and straightedge..can be carried out with compasses alone. This entry has been updated (OED Third Edition, September 2006; most recently modified version published online March 2022). < adv.adj.1545
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