Word Now, by relevance for query the way of shaming machine. Sort by date Show all posts and instead of saying word Named Jesus the word Query includes in Cantore Arithmetic San Francisco word Name Jesus equated word theme[Theme[THEME]].
Cantore Arithmetic is able state words Shaming machine equated word Des Moines as word Named City of Jerusalem equated word Womb, word worm, word sand[Sand], and building a Shaming Machine in my word Sleep is really equated words far-out.
I have a comment. Words, In the good book kjv there is a Book or Chapter on a horror Verse about somebody being cut to word equated word [SHREDS]Shorn and on this Earth word known as CERN in word Initials to worded CERN, the European Organization for Nuclear Research, is one of the world's largest and most respected centres for scientific research to a worded Stain Glass Window and how it is word made, to the Pharaohs word Boxed that are word Covered in word Device that are called words I don’t know however a [word Paper equated word deck[Deck[DECK[tier[Tier[TIER]]]]]]Picture:::
REM Sleep is word equated word HORROR!!!!
Now, for the Equation the Doctors of word Facility are able to type in words, the way of HORROR and the Query of nos however nos is weird do word the Doctors of Psychology that are already in Psychiatry are in the SFO Duty Shop for word health only so the word makings is word pronounced and not word held.
1. 0:15 / 3:51 Resident Evil: Laser scene (HD CLIP)
2. There are Films that show Laser Lights that are usually used in Burglaries of whatever they are trying to word forge
You searched for
"HORROR" in the KJV Bible
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- Psalms 119:53chapter context similar meaning copy save
- Horror hath taken hold upon me because of the wicked that forsake thy law.
- Psalms 55:5chapter context similar meaning copy save
- Fearfulness and trembling are come upon me, and horror hath overwhelmed me.
- Genesis 15:12chapter context similar meaning copy save
- And when the sun was going down, a deep sleep fell upon Abram; and, lo, an horrorof great darkness fell upon him.
- Ezekiel 7:18chapter context similar meaning copy save
- They shall also gird themselves with sackcloth, and horror shall cover them; and shame shall be upon all faces, and baldness upon all their heads.
Words, So, the Crazy Horse word doctor as a word Psychologist only is able to word query, is Des Moines on another word Planet. Words, ONLY THE CRAZY HORSE FACILITIES, HOSPITALS, AND AMA ABBREVIATION AND ANY ASSOCIATED ASSOCIATION WITH DR. BYRON KILGORE OR DR. LOUIS VUKSINICK AND HIS OFFICE are or should be the ONLY ONES INTERESTED IN WORD World as word whirled, word Whirled, word WHIRLED is directly equated word doors, word Doors, word DOORS.
You searched for
"WORLD" in the KJV Bible
249 RESULTS - PAGE 1 OF 9 - SORT BY BOOK ORDER - FEEDBACK
- John 15:19chapter context similar meaning copy save
- If ye were of the world, the world would love his own: but because ye are not of the world, but I have chosen you out of the world, therefore the world hateth you.
- John 3:17chapter context similar meaning copy save
- For God sent not his Son into the world to condemn the world; but that the worldthrough him might be saved.
- John 17:14chapter context similar meaning copy save
- I have given them thy word; and the world hath hated them, because they are not of the world, even as I am not of the world.
- 1 John 4:5chapter context similar meaning copy save
- They are of the world: therefore speak they of the world, and the world heareth them.
- 1 Corinthians 7:31chapter context similar meaning copy save
- And they that use this world, as not abusing it: for the fashion of this world passeth away.
- 1 John 2:15chapter context similar meaning copy save
- Love not the world, neither the things that are in the world. If any man love the world, the love of the Father is not in him.
- Colossians 2:20chapter context similar meaning copy save
- Wherefore if ye be dead with Christ from the rudiments of the world, why, as though living in the world, are ye subject to ordinances,
- John 1:10chapter context similar meaning copy save
- He was in the world, and the world was made by him, and the world knew him not.
- 2 Peter 2:5chapter context similar meaning copy save
- And spared not the old world, but saved Noah the eighth person, a preacher of righteousness, bringing in the flood upon the world of the ungodly;
- 1 John 5:4chapter context similar meaning copy save
- For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith.
- Galatians 6:14chapter context similar meaning copy save
- But God forbid that I should glory, save in the cross of our Lord Jesus Christ, by whom the world is crucified unto me, and I unto the world.
- Hebrews 9:26chapter context similar meaning copy save
- For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself.
- John 16:33chapter context similar meaning copy save
- These things I have spoken unto you, that in me ye might have peace. In the worldye shall have tribulation: but be of good cheer; I have overcome the world.
- James 4:4chapter context similar meaning copy save
- Ye adulterers and adulteresses, know ye not that the friendship of the world is enmity with God? whosoever therefore will be a friend of the world is the enemy of God.
- 1 Corinthians 5:10chapter context similar meaning copy save
- Yet not altogether with the fornicators of this world, or with the covetous, or extortioners, or with idolaters; for then must ye needs go out of the world.
- John 8:23chapter context similar meaning copy save
- And he said unto them, Ye are from beneath; I am from above: ye are of this world; I am not of this world.
- John 17:18chapter context similar meaning copy save
- As thou hast sent me into the world, even so have I also sent them into the world.
- John 17:11chapter context similar meaning copy save
- And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are.
- 1 Corinthians 2:6chapter context similar meaning copy save
- Howbeit we speak wisdom among them that are perfect: yet not the wisdom of this world, nor of the princes of this world, that come to nought:
- John 17:16chapter context similar meaning copy save
- They are not of the world, even as I am not of the world.
- 1 Corinthians 6:2chapter context similar meaning copy save
- Do ye not know that the saints shall judge the world? and if the world shall be judged by you, are ye unworthy to judge the smallest matters?
- John 12:31chapter context similar meaning copy save
- Now is the judgment of this world: now shall the prince of this world be cast out.
- John 18:36chapter context similar meaning copy save
- Jesus answered, My kingdom is not of this world: if my kingdom were of this world, then would my servants fight, that I should not be delivered to the Jews: but now is my kingdom not from hence.
- John 12:47chapter context similar meaning copy save
- And if any man hear my words, and believe not, I judge him not: for I came not to judge the world, but to save the world.
- John 16:28chapter context similar meaning copy save
- I came forth from the Father, and am come into the world: again, I leave the world, and go to the Father.
- 1 Corinthians 1:20chapter context similar meaning copy save
- Where is the wise? where is the scribe? where is the disputer of this world? hath not God made foolish the wisdom of this world?
- 1 John 2:16chapter context similar meaning copy save
- For all that is in the world, the lust of the flesh, and the lust of the eyes, and the pride of life, is not of the Father, but is of the world.
- John 9:5chapter context similar meaning copy save
- As long as I am in the world, I am the light of the world.
- John 13:1chapter context similar meaning copy save
- Now before the feast of the passover, when Jesus knew that his hour was come that he should depart out of this world unto the Father, having loved his own which were in the world, he loved them unto the end.
- Matthew 12:32chapter context similar meaning copy save
- And whosoever speaketh a word against the Son of man, it shall be forgiven him: but whosoever speaketh against the Holy Ghost, it shall not be forgiven him, neither in this world, neither in the world to come.
- Karen Placek
- Presents, a Life with a Plan. My name is Karen Anastasia Placek, I am the author of this Google Blog. This is the story of my journey, a quest to understanding more than myself. The title of my first blog delivered more than a million views!! The title is its work as "The Secret of the Universe is Choice!; know decision" will be the next global slogan. Placed on T-shirts, Jackets, Sweatshirts, it really doesn't matter, 'cause a picture with my slogan is worth more than a thousand words, it's worth??.......Know Conversation!!!
Showing posts sorted by relevance for query the way of shaming machine. Sort by date Show all posts
Friday, December 8, 2017
Morpheus Found: Metamorphosis Is A Theme Or Form Of Alienation Or At First Sight The Horror Of An Alien Neigh Shin!!!
A note to finger the Print to posture in the swatch,
what is the wrap ping should the not sound be math,
as arithmetic seeks & words just verse,
is the sing of monotone a desperate switch?
Sort did off description of noun verses noise,
the echo land to communicate soy,
milk in nature texture be cottage's wheel,
thicken that adding only exit to speak!!
Nostrodamus had an Affinity with bulb bust?,
cycle a challenge and pear a graph the apple,
banana the grape touch thorn with a needle?,
shy are the venue's of virtues a pawn Earth.
Chest piece while check err's gallant Gallon's at quartz,
is it the field of where is that sand?,
or is soil so fertile thus country's in town,
sit deed is promise of more than a found!!
A fingerprint Palm with sweeping Winds create soared,
across that is the void of that plaza each inch is it's bound?,
Pandora must blush as the rouge is in cheeks,
smiling difference while work is in tiled.
The Rule of Thumb,
a golden rule,
book of owe mass stir is church in the pew,
Bankers and in Cents,
a penny of leant east favor of south,
what than is paw should the cat say it cloak?
Virtue signalling
Virtue signalling is the conspicuous expression of moral values done primarily with the intent of enhancing standing within a social group.[1] The term was first used in signalling theory, to describe any behavior that could be used to signal virtue—especially piety among the religious.[2] In recent years, the term has become more commonly used as a pejorative characterization by commentators to criticize what they regard as empty, or superficial support of certain political views, and also used within groups to criticize their own members for valuing outward appearance over substantive action.[3][4] This usage of the term has been criticized for misusing the concept of signalling and encouraging lazy thinking.[5]
Within signalling theory[edit]
Within evolutionary biology, signalling theory is a body of theoretical work examining communication between organisms. It is concerned with honest signals. For example, a peacock's tail is an honest signal of his fitness, since a less fit peacock would only be able to produce a less spectacular tail.
Similarly, signalling is considered within economics. A bank's impressive architecture may serve as a signal of its financial soundness, since a less well-endowed bank could only afford less impressive buildings. Qualifications can signal a person's ability to an employer, even when those qualifications are not strictly necessary, since a less able job applicant will not be able to achieve the same level of qualification.[5]
Unless signalling is considered, costly religious rituals such as circumcision, fasting, and snake handling look paradoxical in both evolutionary and economic terms. Religion may have arisen to increase and maintain intragroup cooperation,[6] and religious traditions include costly rituals, performed publicly, as a hard-to-fake sign of commitment.[7] Such behavior is sometimes described as "virtue signalling".[2]
Pejorative usage[edit]
In the late 2000s, the term began to be redefined on internet forums and social media away from its academic meaning and turned into a pejorative.[citation needed] Examples of behavior described as virtue signalling include changing Facebook profile pictures to support a cause, participation in the Ice Bucket Challenge, offering thoughts and prayers after a tragedy, celebrity speeches during award shows, politicians pandering to constituents on ideological issues, and others.[4]
According to linguist Geoffrey Nunberg, the term is more common among the political right. Lexographer Orin Hargraves says that the term stems from social media, which removes barriers to broadcasting sentiments. Hargrave links the term to the "-shaming" category of neologisms, such as "prayer-shaming", which can have an opposite meaning to virtue signalling. Merriam-Webster editor Emily Brewster described it as an academic-sounding counterpart to "humblebrag," a term coined by Harris Wittels in 2010.[4]
On June 22, 2014, a comment posted on a PJ Media article used the term "Virtue Signalling" to describe several articles critical of a piece by George Will about the US Federal government's reactions to claims of on-campus rape.[10][11]
In April 2015, writing in The Spectator, British author James Bartholomew used the term to describe public, empty gestures intended to convey socially approved attitude without any associated risk or sacrifice.[12] Bartholomew specifically criticized in-store advertising at Whole Foods Market where a picture of a mother carrying her child on her shoulders under the caption "VALUES MATTER...We are part of a growing consciousness that is bigger than food—one that champions what's good."[13][14][15] He stated that "This a particularly blatant example of the increasingly common phenomenon of what might be called 'virtue signalling'—indicating that you are kind, decent and virtuous."[13] He also applied the phrase to several other media, academic, and political figures.[13] According to Bartholomew, virtue signalling can be either declarations of support, or declarations of hate towards negative things, as a way to hide self-aggrandizing intentions of the signal.[16][12][3]
In a later article, Bartholomew incorrectly claimed to have invented the phrase.[17] Bartholomew's claims have been challenged by The Boston Globe[4] and The Guardian, although both credited Bartholomew with popularizing the term.[3]
Commentary[edit]
In a blog post for the Adam Smith Institute, Sam Bowman stated that the meaning of the term popularised by James Bartholomew misuses the concept of signalling and encourages lazy thinking.[5] In The Guardian, Zoe Williams described the phrase as the "sequel insult to champagne socialist",[18] while fellow Guardian writer David Shariatmadari says that while the term serves a purpose, its overuse as an ad hominem attack during political debate has rendered it a meaningless political buzzword.[3] In an article later published by the New Statesman, Tanya Gold claimed that 'people who accuse others of "virtue signalling" are trying to stigmatise empathy', describing it as 'devious political propaganda'.[19]
Helen Lewis, writing for the New Statesman, blamed virtue signalling for the Labour Party's defeat in the 2015 general election, suggesting that the desire to be seen as holding virtuous opinions leads political activists to focus on issues such as nuclear disarmament that are lofty and remote to common voters, resulting in an echo chamber effect that led Labour strategists to underestimate support for Conservative policies.[20]
1.0E. Language and script of the description
When applicable, apply these guidelines, including the use of brackets, to headings.
Table of Contents:
Do not attempt to replicate font features such as bold and italic (e.g., when used to indicate a scientific name) through the use of underlining or other means of indicating such features.
In general, transcribe letters as they appear in the source. However, convert earlier forms of letters and earlier forms of diacritical marks into their modern form, as specified herein. If there is any doubt as to the correct conversion of elements to modern forms, transcribe them from the source as exactly as possible. (See also the section on Special Letters, Diacritical Marks, and Punctuation Marks.)
The following represent a special case: u/v, uu, or vv/w. When these letters are used in Latin and some other languages without regard to their vocalic or consonantal value, so that "u" is used for a "v," etc., the transcription should be regularized. This means that for the bibliographic description of items published after 1800,
1. use v for consonants, e.g., vox, Victoria;
2. use u for vowels, e.g., uva, Ursa Major;
3. use w for consonantal uu or vv, e.g., Windelia.
Follow this guide also for publications of any date when the case is not one of bibliographic description, e.g., headings or citations from reference works.
The letters i/j should be handled differently. For the bibliographic descriptions of items published after 1800, transcribe "i" and "j" as they appear; do not attempt any regularization. PCC practice: Follow this stipulation also for uniform titles for series.
For any other case of headings, citations from reference sources, etc.,
1. use j for consonants, e.g., jus, Julius;
2. use i for vowels, e.g., iter, Ilias.
N.B. For the transcription of any of these letters in bibliographic description for pre-1801 publications, apply Descriptive Cataloging of Rare Materials (Books) (DCRM(B)). For the use of uniform titles, so that DCRM(B) titles file properly (i.e., together with the titles of post-1800 publications), see LCRI 25.1.
The rule, in effect, requires as much fidelity to the source as the technical capacity within the cataloging agency will allow. It recommends a "cataloguer’s description in square brackets" for any "matter that cannot be reproduced by the facilities available." Generally, this is a practicable solution, but there are special instances in which doing other than describing the matter is appropriate. The main purposes of these instructions are to categorize all the methods to be employed, including a "cataloguer’s description," and to give specific directions for each in terms of the particular character set phenomenon encountered.
In the context of machine-readable catalog records note that as used in 1.0E and in the preceding paragraph, "facilities available" means the totality of characters that can be represented in machine-readable form and displayed/printed (known as the "MARC-8 character set"; referred to hereafter as the "character set"). These characters can also be represented in the UCS/Unicode UTF-8 character set, but the guidelines in this LCRIapply only to that subset of the Unicode UTF-8 set that has a counterpart in MARC-8, i.e., the MARC repertoire of UTF-8. Conventions appropriate to particular character set situations have been developed as follows:
Special Marks of Contraction (e.g., older printed Latin)
Apply the appropriate conventions described in the sections below. As judged appropriate, use notes to explain and added entries to provide additional access. In the special provisions below, notes are suggested as possible models for form, not to require the use of the note.
If the super/subscript placement of a character is not essential to avoid serious distortion or loss of intelligibility (e.g., 
, 
, 
), record the super/subscript character on the line in the regular manner (e.g., no., 2e). If a period is associated with the super/subscript letter (e.g., 
) and the characters are the abbreviation of a single word, record the period as the last element (e.g., Ma.). In case of serious distortion or loss of intelligibility, record the character in super/subscript position for all such characters available in the character set, namely, Arabic numerals (0-9), the minus sign ( - ), parentheses ( ( ) ), and the plus sign ( + ). In all other cases use the double underscore convention described in the section on Special Letters, Diacritical Marks, and Punctuation Marks. Give the letter being represented in upper or lower case according to the source.
, , ), record the super/subscript character on the line in the regular manner (e.g., no., 2e). If a period is associated with the super/subscript letter (e.g., ) and the characters are the abbreviation of a single word, record the period as the last element (e.g., Ma.). In case of serious distortion or loss of intelligibility, record the character in super/subscript position for all such characters available in the character set, namely, Arabic numerals (0-9), the minus sign ( - ), parentheses ( ( ) ), and the plus sign ( + ). In all other cases use the double underscore convention described in the section on Special Letters, Diacritical Marks, and Punctuation Marks. Give the letter being represented in upper or lower case according to the source.
In roman script records romanize all occurrences of Greek letters (with the exception below) regardless of the facilities available (the intent is to assist filing and searching even though there are characters for alpha, beta, and gamma in the character set and certain Greek capital letters are identical to their roman equivalents). If the context shows that a Greek letter or letters is used to represent a letter in the International Phonetic Alphabet, however, see the section on Special Letters, Diacritical Marks, and Punctuation Marks.
Exception: If the Greek letter appears separately, give the name of the letter in the language of the context (if unknown in the language of the context, use English) enclosed within brackets. For searching purposes, insure that the bracketed interpolation is not connected with other letters. Thus, if no space appears in the source on either side of the Greek letter, put a space on either side of the bracketed interpolation, except when this interpolation is already distinct from adjacent letters by the presence of characters that serve as separators. N.B. This provision is necessary, because brackets do not serve as separators for searching purposes. ( FN 1)
When a Greek letter is used in a word that is otherwise in the roman alphabet in the source, use the romanized form of the letter (instead of its name) in brackets.
(The letter in this example is from the International Phonetic Alphabet; therefore, the double underscore convention is used (cf. the section on Special Letters, Diacritical Marks, and Punctuation Marks).)
When special marks of contraction have been used by the printer in continuance of the manuscript tradition, expand affected words to their full form, enclosing supplied letters within brackets.
Do not expand conventional abbreviations in which a period follows a letter or letters. However, when an abbreviation standing for an entire word appears in the source, record instead the word itself, enclosing it in brackets, e.g., "... amico[rum] [et] ..." When the meaning of an abbreviation or contraction cannot be determined, substitute a question mark within brackets for each element in question, e.g., "... amico[?] [?] ..." When the meaning of an abbreviation or contraction is conjectural, use the question mark after the supplied letters or word within the same set of brackets, e.g., "...amico[rum?] ..."
When titles are "expanded," title added entries may be generated by the first indicator in the 245 field . The added entry will be exactly the same as the title proper (including the brackets around letters). To express a title added entry in any other form, use a 246 field .
246 3# $a Breviarium monasticum secundum ritum et morem monachorum Ordinis Sancti Benedicti de observantia Casinensis Congregationis
Use the double underscore (
) as the conventional means of signaling special letters (including superscript and subscript letters), diacritical marks, and punctuation marks for which there is no exact representation in the character set. Use the double underscore with the nearest roman equivalent in cases in which the roman equivalent is obvious, e.g., 
. When the nearest roman equivalent is not obvious or there is doubt that it is obvious, it is necessary to establish the equivalent, after which the list of equivalencies will be updated. The equivalencies below have been established to date, mostly from the International Phonetic Alphabet (IPA). Note that the IPA uses some Greek letters; when it is judged by the context (usually some form of linguistic study) that the Greek letter probably derives from its use in the IPA, use the double underscore convention or the equivalency indicated below, not the convention for Greek letters given above.
) as the conventional means of signaling special letters (including superscript and subscript letters), diacritical marks, and punctuation marks for which there is no exact representation in the character set. Use the double underscore with the nearest roman equivalent in cases in which the roman equivalent is obvious, e.g., . When the nearest roman equivalent is not obvious or there is doubt that it is obvious, it is necessary to establish the equivalent, after which the list of equivalencies will be updated. The equivalencies below have been established to date, mostly from the International Phonetic Alphabet (IPA). Note that the IPA uses some Greek letters; when it is judged by the context (usually some form of linguistic study) that the Greek letter probably derives from its use in the IPA, use the double underscore convention or the equivalency indicated below, not the convention for Greek letters given above.
Note that the use of the double underscore convention does not always insure a one-for-one equivalency; the intent, instead, is to signal those cases in which the character used in the catalog record is not an exact replication of the character in the source.
Exception: Do not use the double underscore convention in the following cases; use instead the equivalent indicated:
The objective in treating signs and symbols not represented in the character set is to render or convey the intention without undue time and effort and with a minimum of interpolation, using one of the techniques described in this section. Note that a minimum of interpolation is wanted because those searching the machine catalog cannot very often be expected to "second-guess" the cataloger in this respect, i.e., users will normally formulate search queries that necessarily do not take interpolations into account. As judged appropriate, use notes to explain and added entries to provide additional access; the examples below are illustrative, not prescriptive.
1. If the symbol is judged not to be a integral or essential part of the title, do not intervene in the transcription. Instead, omit the symbol; explain its presence in a note if it is judged worth mentioning.
transcription: 245 10 $a "W" today! Tomorrow?
(On the title page the traditional female symbol appears under the letter "W" but the preface makes it clear that the symbol is not intended to form part of the title and gives the full title.)
suggested note: 500 ## $a On t.p. the symbol for female appears under the letter "W"
added entry: 246 30 $a Women today! Tomorrow?
2. Use existing characters when this can be done without serious distortion or loss of intelligibility.
3. Use the double underscore convention (cf. the section Special Letters, Diacritical Marks, and Punctuation Marks.)
4. Substitute in the language of the context the word, phrase, etc., that is the obvious spoken/written equivalent (if unknown in the language of the context, use English); bracket the interpolated equivalent. If the element in the source is not preceded or followed by a space, in general precede or follow the bracketed interpolation by a space unless the preceding or following character in the source is itself also a separator or unless the use of a space would create an unintended result for searching.
chief source: I 
a piano
a pianotranscription: 245 10 $a I [love] a piano
suggested note: 500 ## $a On t.p. "[love]" appears as a heart
chief source: A study of the 
transcription: 245 12 $a A study of the [ankh]
suggested note: 500 ## $a On t.p. "[ankh]" appears as the ankh symbol
chief source: Poe
and free verse
and free versetranscription: 245 10 $a Poe[try] and free verse
(The interpolation is not preceded by a space because that would create two words for searching (brackets are not separators).)
suggested note: 500 ## $a On t.p. "[try]" appears as an illustration in the form of a tree
chief source: Tinglysningslovens §38
transcription: 245 10 $a Tinglysningslovens [paragraf] 38
chief source: Dokumentation der politischen Geschichte zur Reform des §144 STG
transcription: 245 10 $a Dokumentation der politischen Geschichte zur Reform des [Paragraphen] 144 STG
chief source: ... proposed rules governing §2255 proceedings ...
transcription: 245 10 $a ... $b ... proposed rules governing [section] 2255 proceedings ...
chief source: Roman Opalka : 16 Details aus dem Werk 1965/1-∞
transcription: 245 10 $a Roman Opalka : $b 16 Details aus dem Werk 1965/1-[unendlich]
suggested note: 500 ## $a On t.p. "[unendlich]" appears as the infinity symbol
chief source: Opalka 1965/1-∞ : 9 juin-9 juillet 1982
transcription: 245 10 $a Opalka 1965/1-[l'infinité] : $b 9 juin-9 juillet 1982
suggested note: 500 ## $a On t.p. "[l'infinité]" appears as the infinity symbol
chief source: The added mass coefficient of a cylinder oscillating in shallow water in the limit K→0 and K∞
transcription: 245 14 $a The added mass coefficient of a cylinder oscillating in shallow water in the limit K --> 0 and K [infinity]
(The arrow is input as two hyphens and an angle bracket.)
suggested note: 500 ## $a On t.p. "[infinity]" appears as the infinity symbol
Exception 1: Do not transcribe characters that indicate birth (e.g., an asterisk) or death (e.g., a dagger) even if such characters are in the character set. Do not use a mark of omission; instead, explain the omission in a note.
chief source: In honor of Saint Basil the Great 
379
379transcription: 245 10 $a In honor of Saint Basil the Great 379
suggested note: 500 ## $a On t.p. "379" is preceded by a dagger
chief source: Walter : *1926
1945 an der Ostfront
1945 an der Ostfronttranscription: 245 00 $a Walter : $b 1926 1945 an der Ostfront
suggested note: 500 ## $a On t.p. "1926" is preceded by an asterisk; "1945" is preceded by an Iron Cross
Exception 2: Ignore symbols indicating trademark (registered or otherwise), patent, etc. These include a superscript or subscript "R" enclosed in a circle ( ® ) (ignore although included in the character set) and the superscript or subscript letters "TM" ( ä). Do not explain their presence in a note. (Ignore such symbols also when they appear with elements used in headings.)
chief source: The Gumby® books of letters
transcription: 245 14 $a The Gumby books of letters
If the spoken/written equivalent is not obvious or if there is doubt that it is obvious or if it is unknown, give an explanation or a description in the language of the context (if unknown in the language of the context, use English).
If a title consists solely of a sign or symbol or one or more marks of punctuation, provide an equivalent in all cases, even if the particular symbol is itself in the character set.
chief source: / Gregory Corso
/ Gregory Corsotranscription: 245 10 $a [Ankh] / $c Gregory Corso
suggested note: 500 ## $a The title consists solely of the ankh symbol
chief source: + : [novellaciklus] / Czakó Gábor
transcription: 245 10 $a [Plusz : $b novellaciklus] / $c Czakó Gábor
("+" is in the character set.)
suggested note: 500 ## $a The title consists solely of a plus sign
chief source: © / Free Spirits, Inc.
transcription: 245 10 $a [Copyright] / $c Free Spirits, Inc.
("©" is in the character set.)
suggested note: 500 ## $a The title consists solely of the copyright symbol
chief source: ---- / Edvardas Gudavičius
transcription: 245 10 $a [Keturi brūkšniai] / $c Edvardas Gudavičius.
suggested note: 500 ## $a The title consists solely of four hyphens
but
chief source: ????? Steele's answers, by Daniel Steele ...
transcription: 245 10 $a ????? Steele's answers / $c by Daniel Steele ...
(Although the title begins with marks of punctuation, it also contains indexable data and no special intervention is required.)
See also:
Euler's formula
| Part of a series of articles on the |
| mathematical constant e |
|---|
 |
| Properties |
| Applications |
| Defining e |
| People |
| Related topics |
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x
where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sinerespectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.[1]
Euler's formula is ubiquitous in mathematics, physics, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics".[2]
Contents
[hide]History[edit]
Johann Bernoulli noted that[3]
And since
the above equation tells us something about complex logarithms by relating natural logarithms to imaginary (complex) numbers. Bernoulli, however, did not evaluate the integral.
Bernoulli's correspondence with Euler (who also knew the above equation) shows that Bernoulli did not fully understand complex logarithms. Euler also suggested that the complex logarithms can have infinitely many values.
Meanwhile, Roger Cotes in 1714 discovered that[4]
Cotes missed the fact that a complex logarithm can have infinitely many values, differing by multiples of 2iπ, due to the periodicity of the trigonometric functions.
Around 1740 Euler turned his attention to the exponential function instead of logarithms and obtained the formula used today that is named after him. It was published in 1748, obtained by comparing the series expansions of the exponential and trigonometric expressions.[5][4]
The view of complex numbers as points in the complex plane was described about 50 years later by Caspar Wessel.
Applications in complex number theory[edit]
- Interpretation of the formula
This formula can be interpreted as saying that the function eiφ is a unit complex number, i.e., it traces out the unit circle in the complex planeas φ ranges through the real numbers. Here φ is the angle that a line connecting the origin with a point on the unit circle makes with the positive real axis, measured counterclockwise and in radians.
The original proof is based on the Taylor series expansions of the exponential function ez (where z is a complex number) and of sin x and cos x for real numbers x (see below). In fact, the same proof shows that Euler's formula is even valid for all complex numbers x.
A point in the complex plane can be represented by a complex number written in cartesian coordinates. Euler's formula provides a means of conversion between cartesian coordinates and polar coordinates. The polar form simplifies the mathematics when used in multiplication or powers of complex numbers. Any complex number z = x + iy, and its complex conjugate, z = x − iy, can be written as
where
- x = Re z is the real part,
- y = Im z is the imaginary part,
- r = |z| = √x2 + y2 is the magnitude of z
- φ = arg z = atan2(y, x).
φ is the argument of z, i.e., the angle between the x axis and the vector z measured counterclockwise in radians, which is defined up to addition of 2π. Many texts write φ = tan−1 yx instead of φ = atan2(y,x), but the first equation needs adjustment when x ≤ 0. This is because for any real x and y not both zero the angles of the vectors (x, y) and (−x, −y)differ by π radians, but have the identical value of tan φ = yx.
- Use of the formula to define the logarithm of complex numbers
Now, taking this derived formula, we can use Euler's formula to define the logarithm of a complex number. To do this, we also use the definition of the logarithm (as the inverse operator of exponentiation):
and that
both valid for any complex numbers a and b.
Therefore, one can write:
for any z ≠ 0. Taking the logarithm of both sides shows that
and in fact this can be used as the definition for the complex logarithm. The logarithm of a complex number is thus a multi-valued function, because φ is multi-valued.
Finally, the other exponential law
which can be seen to hold for all integers k, together with Euler's formula, implies several trigonometric identities, as well as de Moivre's formula.
Relationship to trigonometry[edit]
Euler's formula provides a powerful connection between analysis and trigonometry, and provides an interpretation of the sine and cosine functions as weighted sums of the exponential function:
The two equations above can be derived by adding or subtracting Euler's formulas:
and solving for either cosine or sine.
These formulas can even serve as the definition of the trigonometric functions for complex arguments x. For example, letting x = iy, we have:
Complex exponentials can simplify trigonometry, because they are easier to manipulate than their sinusoidal components. One technique is simply to convert sinusoids into equivalent expressions in terms of exponentials. After the manipulations, the simplified result is still real-valued. For example:
Another technique is to represent the sinusoids in terms of the real part of a complex expression and perform the manipulations on the complex expression. For example:
![{\displaystyle {\begin{aligned}\cos(nx)&=\operatorname {Re} \left(e^{inx}\right)\\&=\operatorname {Re} \left(e^{i(n-1)x}\cdot e^{ix}\right)\\&=\operatorname {Re} {\Big (}e^{i(n-1)x}\cdot {\big (}\underbrace {e^{ix}+e^{-ix}} _{2\cos x}-e^{-ix}{\big )}{\Big )}\\&=\operatorname {Re} \left(e^{i(n-1)x}\cdot 2\cos x-e^{i(n-2)x}\right)\\&=\cos[(n-1)x]\cdot [2\cos(x)]-\cos[(n-2)x].\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/337400ddab1ffe801d4e8e73c86f7a9f446a79d4)
This formula is used for recursive generation of cos nx for integer values of n and arbitrary x (in radians).
See also Phasor arithmetic.
Topological interpretation[edit]
In the language of topology, Euler's formula states that the imaginary exponential function t ↦ eit is a (surjective) morphism of topological groups from the real line ℝ to the unit circle 1. In fact, this exhibits ℝ as a covering space of 1. Similarly, Euler's identity says that the kernel of this map is τℤ, where τ = 2π. These observations may be combined and summarized in the commutative diagram below:
Other applications[edit]
In differential equations, the function eix is often used to simplify solutions, even if the final answer is a real function involving sine and cosine. The reason for this is that the exponential function is the eigenfunction of the operation of differentiation.
In electrical engineering, signal processing, and similar fields, signals that vary periodically over time are often described as a combination of sinusoidal functions (see Fourier analysis), and these are more conveniently expressed as the sum of exponential functions with imaginary exponents, using Euler's formula. Also, phasor analysis of circuits can include Euler's formula to represent the impedance of a capacitor or an inductor.
In the four-dimensional space of quaternions, there is a sphere of imaginary units. For any point r on this sphere, and x a real number, Euler's formula applies:
and the element is called a versor in quaternions. The set of all versors forms a 3-sphere in the 4-space.
Definitions of complex exponentiation[edit]
The exponential function ex for real values of x may be defined in a few different equivalent ways (see Characterizations of the exponential function). Several of these methods may be directly extended to give definitions of ez for complex values of z simply by substituting z in place of x and using the complex algebraic operations. In particular we may use either of the two following definitions, which are equivalent. From a more advanced perspective, each of these definitions may be interpreted as giving the unique analytic continuation of exto the complex plane.
Power series definition[edit]
For complex z
Using the ratio test, it is possible to show that this power series has an infinite radius of convergence and so defines ez for all complex z.
Limit definition[edit]
For complex z
Proofs[edit]
Various proofs of the formula are possible.
Using power series[edit]
Here is a proof of Euler's formula using power-series expansions, as well as basic facts about the powers of i:[6]
Using now the power-series definition from above, we see that for real values of x
![{\displaystyle {\begin{aligned}e^{ix}&=1+ix+{\frac {(ix)^{2}}{2!}}+{\frac {(ix)^{3}}{3!}}+{\frac {(ix)^{4}}{4!}}+{\frac {(ix)^{5}}{5!}}+{\frac {(ix)^{6}}{6!}}+{\frac {(ix)^{7}}{7!}}+{\frac {(ix)^{8}}{8!}}+\cdots \\[8pt]&=1+ix-{\frac {x^{2}}{2!}}-{\frac {ix^{3}}{3!}}+{\frac {x^{4}}{4!}}+{\frac {ix^{5}}{5!}}-{\frac {x^{6}}{6!}}-{\frac {ix^{7}}{7!}}+{\frac {x^{8}}{8!}}+\cdots \\[8pt]&=\left(1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-{\frac {x^{6}}{6!}}+{\frac {x^{8}}{8!}}-\cdots \right)+i\left(x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \right)\\[8pt]&=\cos x+i\sin x.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/876f74f43699f5c15b79cb61fa3eec2dbb427837)
In the last step we have simply recognized the Maclaurin series for cos x and sin x. The rearrangement of terms is justified because each series is absolutely convergent.
Using calculus[edit]
Another proof[7] is based on the fact that all complex numbers can be expressed in polar coordinates. Therefore, for some r and θ depending on x,
No assumptions are being made about r and θ; they will be determined in the course of the proof. From any of the definitions of the exponential function it can be shown that the derivative of eix is ieix. Therefore, differentiating both sides gives
Substituting r(cos θ + i sin θ) for eix and equating real and imaginary parts in this formula gives drdx = 0 and dθdx = 1. Thus, r is a constant, and θ is x + C for some constant C. The initial values r(0) = 1 and θ(0) = 0 come from e0i = 1, giving r = 1 and θ = x. This proves the formula
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