每日一词:hapless(转自 韦氏词典)

原文链接


Merriam-Webster’s Word of the Day for July 24, 2019 is:

hapless • \HAP-lus\  • adjective

: having no luck : unfortunate

Examples:

“Whatever your view of Team USA’s rout over Thailand or the way they celebrated every goal over that hapless opponent, the 13-0 opening victory fueled conversation and interest for Sunday’s United States-Chile match.” — Phil Rosenthal, The Chicago Tribune, 18 June 2019

“David Bareford got into violence design when he was living in Chicago and struggling along as ‘an OK actor in a town where there were a million OK actors….’ He decided not to fight those odds; instead he embraced the stage-combat skills that came from acting in Shakespeare tragedies, which usually involve kings, soldiers and other hapless figures eagerly running one another through.” — Scott Hewitt, The Columbian (Vancouver, Washington), 13 June 2019

Did you know?

Hapless literally means what you’d expect it to mean: “without hap”—hap being another word for fortune or luck. Hap derives from the Old Norse word for “good luck,” a word that is also the source of our happen and happy. English has several words to describe those lacking good fortune, including ill-starred, ill-fated, unlucky, and luckless, a word formed in parallel to hapless by adding the suffix -less. Ill-starred suggests bringing calamity or the threat of a terrible fate (“the ill-starred year the Great Depression began”). Ill-fated refers only to being doomed (“the ill-fated voyage of the Titanic”). Unlucky and luckless usually apply to a person or thing notably or chronically unfortunate (“an unlucky slots player,” “some luckless investors swindled in the deal”).


Lake桑

July 24, 2019 at 01:00PM

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每日一词:desideratum(转自 韦氏词典)

原文链接


Merriam-Webster’s Word of the Day for July 23, 2019 is:

desideratum • \dih-sid-uh-RAH-tum\  • noun

: something desired as essential

Examples:

“The strength of his class depended to some extent on sound money management—but depended to a much larger extent on marriages based cynically on the sorts of children likely to be produced. Healthy, charming, wise children were the desiderata.” — Kurt Vonnegut, Jr., The Sirens of Titan, 1959

“The year was 1953, and most American children were secretly wishing, praying and writing letters to Santa Claus promising to be nice rather than naughty in return for that ultimate desideratum of gifts: the ‘real, live pony.'” — Ken Jennings, The Petoskey (Michigan) News-Review, 24 Dec. 2014

Did you know?

We’d like to introduce you to some close cousins of the common word desire. All trace their roots to the Latin sīder-, or sīdus, which has historically been understood to mean “heavenly body,” but which may also have an older, non-celestial meaning of “mark, target, goal.” Whether etymologically starry or grounded, dēsīderāre, meaning “to long for,” was born when Latin de- was prefixed to sīder-. Dēsīderāre begat Anglo-French desirer, which in turn brought forth English desire, desirous, and desirable in the 13th and 14th centuries, with desideration following in the 15th. Then, in the 17th century, English acquired desiderate (“to wish for”) and desideratum (desiderata in the plural), all of which can lay claim to direct ancestry from desiderare.


Lake桑

July 23, 2019 at 01:00PM

每日一词:whinge(转自 韦氏词典)

原文链接


Merriam-Webster’s Word of the Day for July 22, 2019 is:

whinge • \WINJ\  • verb

British : to complain fretfully : whine

Examples:

“I was angry, I went home to my wife and I complained. I was whinging an Olympic level of whinging to Deb, my wife, and moaning about this person and that person.” — Hugh Jackman, quoted in MailOnline, 4 June 2019

“For those who whinged that the Freddie Mercury biopic ‘Bohemian Rhapsody’ played fast and loose with the facts and the timeline—and I was one—it must be said that director Dexter Fletcher’s Elton John movie ‘Rocketman’ takes even more liberties with truth.” — Jim Sullivan, WBUR.org, 31 May 2019

Did you know?

Whinge isn’t a simple spelling variant of whine. Whinge and whine are actually entirely different words with separate histories. Whine traces to an Old English verb, hwinan, which means “to make a humming or whirring sound.” When hwinan became whinen in Middle English, it meant “to wail distressfully”; whine didn’t acquire its “complain” sense until the 16th century. Whinge, on the other hand, comes from a different Old English verb, hwinsian, which means “to wail or moan discontentedly.” Whinge retains that original sense today, though nowadays it puts less emphasis on the sound of the complaining and more on the discontentment behind the complaint.


Lake桑

July 22, 2019 at 01:00PM

数学相关:求抽象函数定义域

初中我们就接触过函数,现在我们把它用高中的语言再说一遍。

A,B是两个给定的非空数集,按照某种确定的对应关系f,使得对于集合A中的任意一个数x,在集合B中都有唯一的数f\left(x\right)与之对应,我们把这种对应f:x\to y=f\left(x\right),x\in A叫做从集合A到集合B的一个函数,记作y=f\left(x\right),x\in D,若省略定义域,则指使函数有意义的一切实数所组成的集合。

函数有两种形式,一种是具体的,即有解析式的,另一种是我们今天重点说的,抽象的,即没有具体解析式的。函数有三个要素,定义域对应法则值域。以及四个性质,单调性奇偶性周期性对称性

这篇文章会先把前三个讲掉。

首先是三个要素。如果两个函数的三要素都完全相同,那么这两个函数相等。其中,定义域指该函数的有效取值范围,即使函数有意义的自变量的范围。一般来说,一个函数的取值范围都是比较连续的,可以用一个范围来表示。比如自变量从3到5,5可以取到而3取不到,就可以写成\left\{x\mid 3<x\leq 5\right\},或者使用区间来表示就是\left(3,5\right]。如果19以上的值都可以取并且包括19,区间就可以写成\left[19,+\infty\right)。即任意描述法中的条件是不等式的集合,都可以写成一个区间。一个不等式中,不带等号的一端用圆括号(小括号),带等号的一端用方括号(中括号)。特别地无穷的那一端只用圆括号[1]。实数集\mathbb{R}就可以表示为\left(-\infty,+\infty\right)。但是如果一个函数的取值不连续,比如从1到2,从5到6都可以,其中2和5可以取,但是其他不行,此时一个区间便不行了,我们要用集合的运算,并集运算,来表示,即\left(1,2\right]\cup\left[5,6\right)。对于\left\{x\mid x\neq 2,x\neq3\right\}则可以写为\left(-\infty,2\right)\cup\left(2,3\right)\cup\left(3,+\infty\right)

[1]:Photomath中使用尖角括号。不同国家可能有不同标准。

如果我们知道了一个函数的解析式,我们可以直接观察表达式。初中学过的共有三个:

  • 分式中的分母不为零
  • 偶次根式的被开方数大于等于零
  • 零次幂的底数不为零

比如求函数f\left(x\right)=\dfrac{\left(2x+3\right)^0}{\sqrt{\left|x\right|-x}}的定义域。

观察可得\begin{cases} 2x+3\neq 0\\ \left|x\right|-x\geq 0\\ \left|x\right|-x\neq 0 \end{cases}

解得\left(-\infty,-\frac{3}{2}\right)\cup\left(-\frac{3}{2},0\right)

现在我们来思考一个问题。

f\left(x\right)=\sqrt{x},可得x\geq 0

代入两个代数式,可得

f\left(2x+1\right)=\sqrt{2x+1},2x+1\geq 0.

f\left(3x-2\right)=\sqrt{3x-2},3x-2\geq 0.

现在我们遮掉所有的解析式,可得f\left(g\left(x\right)\right)g\left(x\right)的取值范围,同时也是f\left(h\left(x\right)\right)h\left(x\right)的取值范围。有必要注意的是,定义域是指x的取值范围,所以我们要从x的范围中反推出一个关于g\left(x\right)的不等式,再将其替换为h\left(x\right)

比如,已知函数f\left(x+1\right)的定义域为\left[2,3\right),求f\left(2x-1\right)的定义域。

\because f\left(x+1\right)的定义域为\left[2,3\right)

\therefore 2\leq x<3.

\therefore 3\leq x+1<4.

\therefore 3\leq 2x-1<4.

解得2\leq x<\dfrac{5}{2}.

\therefore f\left(2x-1\right)的定义域为\left[2,\dfrac{5}{2}\right).

讲完了拜。

Lake桑

2019.7.22

又一个周一。

一周又开始了。加油工作!(由 IFTTT 发送)

Lake桑

July 22, 2019 at 07:00AM

每日一词:redaction(转自 韦氏词典)

原文链接


Merriam-Webster’s Word of the Day for July 21, 2019 is:

redaction • \rih-DAK-shun\  • noun

1 a : an act or instance of preparing something for publication 

b : an act or instance of obscuring or removing something from a document prior to publication or release

2 : a work that has been redacted : editionversion

Examples:

“The city released Craddock’s emailed resignation, but redacted the send and receive times as well as the recipients. A city attorney said the entire document is considered a personnel record and is subject to redaction under the state’s Freedom of Information Act.” — Alissa Skelton, The Virginian-Pilot (Norfolk, Virginia), 14 June 2019

“The black redaction box is meant to protect sensitive information from public view. It’s supposed to be an impenetrable curtain. But sometimes that curtain is surprisingly easy to raise.” — Phillip Bantz, Law.com, 19 Dec. 2018

Did you know?

Here’s a quiz for all you etymology buffs. Can you pick the words from the following list that come from the same Latin root?

A. redaction B. prodigal C. agent D. essay
E. navigate F. ambiguous

If you guessed all of them, you are right. Now, for bonus points, name the Latin root that they all have in common. If you knew that it is the verb agere, meaning to “to drive, lead, act, or do,” you get an A+. Redaction is from the Latin verb redigere (“to bring back” or “to reduce”), which was formed by adding the prefix red- (meaning “back”) to agere. Some other agere offspring include act, agenda, cogent, litigate, chasten, agile, and transact.


Lake桑

July 21, 2019 at 01:00PM

每日一词:cogent(转自 韦氏词典)

原文链接


Merriam-Webster’s Word of the Day for July 20, 2019 is:

cogent • \KOH-junt\  • adjective

1 a : appealing forcibly to the mind or reason : convincing

b : pertinent, relevant

2 : having power to compel or constrain

Examples:

At the town meeting, citizens presented many cogent arguments in support of building a new senior center.

“The council made the difficult decision to raise property taxes by a total of 6 cents…. [The] decision to earmark the full 4 cents for educational capital expenditures was a difficult one, and there were cogent, logical arguments to be made in favor of keeping the city’s options open regarding the use of funds.” — Kate McConnell and Anthony Smith, The Roanoke (Virginia) Times, 21 Apr. 2019

Did you know?

“Trained, knowledgeable agents make cogent suggestions … that make sense to customers.” It makes sense for us to include that comment from the president of a direct marketing consulting company because it provides such a nice opportunity to point out the etymological relationship between the words cogent and agent. Agent derives from the Latin verb agere, which means “to drive,” “to lead,” or “to act.” Adding the prefix co- to agere gave Latin cogere, a word that literally means “to drive together”; that ancient term ultimately gave English cogent. Something that is cogent figuratively pulls together thoughts and ideas, and the cogency of an argument depends on the driving intellectual force behind it.


Lake桑

July 20, 2019 at 01:00PM