# Preface

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters~6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter~8 is accessible after completion of Chapters~1–5.

Without taking a position for or against the current reforms in mathematics teaching, I think it is fair to say that the transition from elementary courses such as calculus, linear algebra, and differential equations to a rigorous real analysis course is a bigger step today than it was just a few years ago. To make this step today’s students need more help than their predecessors did, and must be coached and encouraged more. Therefore, while striving throughout to maintain a high level of rigor, I have tried to write as clearly and informally as possible. In this connection I find it useful to address the student in the second person. I have included 295 completely worked out examples to illustrate and clarify all major theorems and definitions.

I have emphasized careful statements of definitions and theorems and have tried to be complete and detailed in proofs, except for omissions left to exercises. I give a thorough treatment of real-valued functions before considering vector-valued functions. In making the transition from one to several variables and from real-valued to vector-valued functions, I have left to the student some proofs that are essentially repetitions of earlier theorems. I believe that working through the details of straightforward generalizations of more elementary results is good practice for the student.

• Chapter 1 is concerned with the real number system. Section~1.1 begins with a brief discussion of the axioms for a complete ordered field, but no attempt is made to develop the reals from them; rather, it is assumed that the student is familiar with the consequences of these axioms, except for one: completeness. Since the difference between a rigorous and nonrigorous treatment of calculus can be described largely in terms of the attitude taken toward completeness, I have devoted considerable effort to developing its consequences. Section~1.2 is about induction. Although this may seem out of place in a real analysis course, I have found that the typical beginning real analysis student simply cannot do an induction proof without reviewing the method. Section~1.3 is devoted to elementary set theory and the topology of the real line, ending with the Heine-Borel and Bolzano-Weierstrass theorems.
• Chapter~2 covers the differential calculus of functions of one variable: limits, continuity, differentiablility, L’Hospital’s rule, and Taylor’s theorem. The emphasis is on rigorous presentation of principles; no attempt is made to develop the properties of specific elementary functions. Even though this may not be done rigorously in most contemporary calculus courses, I believe that the student’s time is better spent on principles rather than on reestablishing familiar formulas and relationships.
• Chapter~3 is to devoted to the Riemann integral of functions of one variable. In Section~3.1 the integral is defined in the standard way in terms of Riemann sums. Upper and lower integrals are also defined there and used in Section~3.2 to study the existence of the integral. Section~3.3 is devoted to properties of the integral. Improper integrals are studied in Section~3.4. I believe that my treatment of improper integrals is more detailed than in most comparable textbooks. A more advanced look at the existence of the proper Riemann integral is given in Section~3.5, which concludes with Lebesgue’s existence criterion. This section can be omitted without compromising the student’s preparedness for subsequent sections.
• Chapter~4 treats sequences and series. Sequences of constant are discussed in Section~4.1. I have chosen to make the concepts of limit inferior and limit superior parts of this development, mainly because this permits greater flexibility and generality, with little extra effort, in the study of infinite series. Section~4.2 provides a brief introduction to the way in which continuity and differentiability can be studied by means of sequences. Sections~4.3–4.5 treat infinite series of constant, sequences and infinite series of functions, and power series, again in greater detail than in most comparable textbooks. The instructor who chooses not to cover these sections completely can omit the less standard topics without loss in subsequent sections.
• Chapter~5 is devoted to real-valued functions of several variables. It begins with a discussion of the toplogy of (mathbb{R}^{n}) in Section~5.1. Continuity and differentiability are discussed in Sections~5.2 and 5.3. The chain rule and Taylor’s theorem are discussed in Section~5.4.
• Chapter~6 covers the differential calculus of vector-valued functions of several variables. Section~6.1 reviews matrices, determinants, and linear transformations, which are integral parts of the differential calculus as presented here. In Section~6.2 the differential of a vector-valued function is defined as a linear transformation, and the chain rule is discussed in terms of composition of such functions. The inverse function theorem is the subject of Section~6.3, where the notion of branches of an inverse is introduced. In Section~6.4. the implicit function theorem is motivated by first considering linear transformations and then stated and proved in general.
• Chapter~7 covers the integral calculus of real-valued functions of several variables. Multiple integrals are defined in Section~7.1, first over rectangular parallelepipeds and then over more general sets. The discussion deals with the multiple integral of a function whose discontinuities form a set of Jordan content zero. Section~7.2 deals with the evaluation by iterated integrals. Section~7.3 begins with the definition of Jordan measurability, followed by a derivation of the rule for change of content under a linear transformation, an intuitive formulation of the rule for change of variables in multiple integrals, and finally a careful statement and proof of the rule. The proof is complicated, but this is unavoidable.
• Chapter~8 deals with metric spaces. The concept and properties of a metric space are introduced in Section~8.1. Section~8.2 discusses compactness in a metric space, and Section~8.3 discusses continuous functions on metric spaces.

Corrections–mathematical and typographical–are welcome and will be incorporated when received.

## What Is a Preface? How to Introduce Your Book to the World

When writing a nonfiction book, it’s not just the main contents that matter. You also have to pay careful attention to the front matter of your book.

Think of the preface as your book’s chance to make a great first impression (in addition to your beautifully designed cover, of course!).

If you are just building your author platform and people don’t really know you yet, they will be more likely to check out things like the preface, foreword, or featured reviews to get a better feel for your work—so if you include a preface, make it count!

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Children reading proficiently by 3rd grade are 4x less likely to drop out of school.

mv2.png/v1/fill/w_92,h_91,al_c,usm_0.66_1.00_0.01,blur_3/60x.png" />

. and are 60x less likely than their peers to spend time in prison.

\$292,000 each in public assistance and correctional funding!

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Note: Letter-based literacy scores quantified and standardized utilizing equalized interval scale methodology. Improvement quantified based on variation from starting level and evaluated using standard benchmarking.

Data obtained and utilized in accordance with applicable data sharing guidelines of partner institutions.

Source: Preface, Governor&rsquos Books from Birth Foundation, Edmentum, Northeastern University, National Center for Education Statistics.

## Example of a dissertation preface

Published on October 13, 2015 by Sarah Vinz. Revised on March 24, 2017.

The interactive example shows what a preface (or foreword) to a dissertation may look like. The basic guidelines for writing a preface have all been followed.

In the preface, you can talk about your experience in writing your dissertation and thank the people helped you. The first person voice (“I”) is commonly used, as in this example. The trick is to write the preface in a style that is personal yet still professional.

Before you lies the dissertation “Corporate Communication: What is it?”, the basis of which is a survey on corporate communications that was conducted among several municipalities. It has been written to fulfill the graduation requirements of the Communications Program at the Fontys Tilburg School of Economics (FEHT). I was engaged in researching and writing this dissertation from January to June 2014.

The project was undertaken at the request of Central P., where I undertook an internship. My research question was formulated together with my supervisor, Phoebe Buffay. The research was difficult, but conducting extensive investigation has allowed me to answer the question that we identified. Fortunately, both Ms. Buffay and my tutors from the FEHT, Messrs C. Bing and R. Geller, were always available and willing to answer my queries.

I would like to thank my supervisors for their excellent guidance and support during this process. I also wish to thank all of the respondents, without whose cooperation I would not have been able to conduct this analysis.

To my other colleagues at Central P.: I would like to thank you for your wonderful cooperation as well. It was always helpful to bat ideas about my research around with you. I also benefitted from debating issues with my friends and family. If I ever lost interest, you kept me motivated. My parents deserve a particular note of thanks: your wise counsel and kind words have, as always, served me well.

This should be easy after writing a book! This section of the frontmatter can be as short or as long as you’d like. It’s a place to be honest and open with your readers about the writing of the book – be it a fictional, romance novel or a biography of Abraham Lincoln. With interest in the book comes an interest in the author and how they created the work, so readers are naturally drawn to the preface.

Keep these things in mind when writing:

• Writing a book is hard work, and this is the place to talk about that.
• How your book came to life is a journey in itself. Showcase it.
• Make it clear to the reader why they should read the book. The preface is a good marketing tool.

## How to Write a Preface

A preface gives you a chance, before your story begins in earnest, to speak directly to your readers about the reasons why you wrote this book, and to provide a little background information on what they can expect from this story and why they’ll find it interesting.

It’s important to note that not every book needs a preface. However, if you feel like you have some valuable input to provide your readers, the preface is the perfect place for your thoughts. If you think that a preface will be a great addition to your book, check out these four ideas to get you started.

Why did you write the book?

When it comes to writing, there’s always a why. The preface is where you can let your readers in on what motivated you to write the book they are about to read. Has it always been a dream of yours to become a published author? Do you feel so passionately about a subject that you had to share it with the world? Discuss how the book came to be and briefly touch on your writing journey and how it turned into the book that’s in your readers’ hands.

We all gain inspiration from various sources. Whether it’s a mentor, family member, or even a life-changing experience, inspiration is everywhere. The preface is where you can speak about who or what inspired you to write the book. We all want to relate with others, so talk about your inspiration so that you can form an emotional connection with your readers.

Think of the preface as a movie trailer of sorts. It’s here that you’ll be able to give your readers some behind-the-scenes details of what they can expect from your book. Be sure not to give away too much information! But consider including a brief description about your characters and the overall plot. Essentially, use the preface to provide your readers with a teaser of the general synopsis of your book.

Keep it concise.

You don’t want your preface to be a book in and of itself. Be sure to keep it simple and steer clear of long, drawn-out explanations. Cover the basics, but don’t dive into too much detail. Think of the preface as an appetizer. You don’t want to spoil their meal (the book) before dinner is even served!

The preface is an introduction to your book so keep these four ideas in mind to help you get started.

## Preface

Below is the Foreword and Preface to the New American Standard Bible as it appeared in the 1995 edition. I have noted omissions from the previous editions in square brackets and have indicated additions with red type. &mdashM.D.M.

### FOREWORD

#### SCRIPTURAL PROMISE

"The grass withers, the flower fades, but the word of our God stands forever." Isaiah 40:8

The New American Standard Bible has been produced with the conviction that the words of Scripture as originally penned in the Hebrew, Aramaic, and Greek were inspired by God. Since they are the eternal Word of God, the Holy Scriptures speak with fresh power to each generation, to give wisdom that leads to salvation, that men may serve Christ to the glory of God.

The purpose of the Editorial Board in making this translation was to adhere as closely as possible to the original languages of the Holy Scriptures, and to make the translation in a fluent and readable style according to current English usage.

#### THE FOURFOLD AIM OF THE LOCKMAN FOUNDATION

1. These publications shall be true to the original Hebrew, Aramaic, and Greek. 2. They shall be grammatically correct. 3. They shall be understandable. [previous editions read "understandable to the masses"] 4. They shall give the Lord Jesus Christ His proper place, the place which the Word gives Him therefore, no work will ever be personalized.

### PREFACE TO THE NEW AMERICAN STANDARD BIBLE

In the history of English Bible translations, the King James Version is the most prestigious. This time-honored version of 1611, itself a revision of the Bishops' Bible of 1568, became the basis for the English Revised Version appearing in 1881 (New Testament) and 1885 (Old Testament). The American counterpart of this last work was published in 1901 as the American Standard Version. The ASV, a product of both British and American scholarship, has been highly regarded for its scholarship and accuracy. [earlier editions read, "it has frequently been used as a standard for other translations. It is still recognized as a valuable tool for study of the Scriptures"] Recognizing the values of the American Standard Version, the Lockman Foundation felt an urgency to preserve these and other lasting values of the ASV by incorporating recent discoveries of Hebrew and Greek textual sources and by rendering it into more current English. Therefore, in 1959 a new translation project was launched, based on the time-honored principles of translation of the ASV and KJV . The result is the New American Standard Bible.

Translation work for the NASB was begun in 1959. In the preparation of this work numerous other translations have been consulted along with the linguistic tools and literature of biblical scholarship. Decisions about English renderings were made by consensus of a team composed of educators and pastors. Subsequently, review and evaluation by other Hebrew and Greek scholars outside the Editorial Board were sought and carefully considered.

The Editorial Board has continued to function since publication of the complete Bible in 1971. This edition of the NASB represents revisions [previous editions read, "minor revisions"] and refinements recommended over the last several years as well as thorough research based on modern English usage.

#### PRINCIPLES OF TRANSLATION

MODERN ENGLISH USAGE: The attempt has been made to render the grammar and terminology in contemporary English. When it was felt that the word-for-word literalness was unacceptable to the modern reader, a change was made in the direction of a more current English idiom. In the instances where this has been done, the more literal rendering has been indicated in the notes. There are a few exceptions to this procedure. In particular, frequently "And" is not translated at the beginning of sentences because of differences in style between ancient and modern writing. Punctuation is a relatively modern invention, and ancient writers often linked most of their sentences with "and" or other connectives. Also, the Hebrew idiom "answered and said" is sometimes reduced to "answered" or "said" as demanded by the context. For current English the idiom "it came about that" has not been translated in the New Testament except when a major transition is needed.

ALTERNATIVE READINGS: In addition to the more literal renderings, notations have been made to include alternate translations, reading of variant manuscripts and explanatory equivalents of the text. Only such notations have been used as have been felt justified in assisting the reader's comprehension of the terms used by the original author.

HEBREW TEXT: In the present translation the latest edition of Rudolf Kittel's BIBLIA HEBRAICA has been employed together with the most recent light from lexicography, cognate languages, and the Dead Sea Scrolls.

HEBREW TENSES: Consecution of tenses in Hebrew remains a puzzling factor in translation. The translators have been guided by the requirements of a literal translation, the sequence of tenses, and the immediate and broad contexts.

THE PROPER NAME OF GOD IN THE OLD TESTAMENT: In the Scriptures, the name of God is most significant and understandably so. It is inconceivable to think of spiritual matters without a proper designation for the Supreme Deity. Thus the most common name for the Deity is God, a translation of the original Elohim. One of the titles for God is Lord, a translation of Adonai. There is yet another name which is particularly assigned to God as His special or proper name, that is, the four letters YHWH (Exodus 3:14 and Isaiah 42:8). This name has not been pronounced by the Jews because of reverence for the great sacredness of the divine name. Therefore, it has been consistently translated LORD. The only exception to this translation of YHWH is when it occurs in immediate proximity to the word Lord, that is, Adonai. In that case it is regularly translated GOD in order to avoid confusion. It is known that for many years YHWH has been transliterated as Yahweh, however no complete certainty attaches to this pronunciation.

GREEK TEXT: Consideration was given to the latest available manuscripts with a view to determining the best Greek text. In most instances the 26th edition [previous editions read, "23rd edition"] of Eberhard Nestle's NOVUM TESTAMENTUM GRAECE was followed.

GREEK TENSES: A careful distinction has been made in the treatment of the Greek aorist tense (usually translated as the English past, "He did") and the Greek imperfect tense (normally rendered either as English past progressive, "He was doing" or, if inceptive, as "He began to do" or "He started to do" or else if customary past, as "He used to do"). "Began" is italicized if it renders an imperfect tense, in order to distinguish it from the Greek verb for "begin." In some contexts the difference between the Greek imperfect and the English past is conveyed better by the choice of vocabulary or by other words in the context, and in such cases the Greek imperfect may be rendered as a simple past tense (e.g. "had an illness for many years" would be preferable to "was having an illness for many years" and would be understood in the same way).

On the other hand, not all aorists have been rendered as English pasts ("He did"), for some of them are clearly to be rendered as English perfects ("He has done"), or even as past perfects ("He had done"), judging from the context in which they occur. Such aorists have been rendered as perfects or past perfects in this translation.

As for the distinction between aorist and present imperatives, the translators have usually rendered these imperatives in the customary manner, rather than attempting any such fine distinction as "Begin to do!" (for the aorist imperative), or, "Continually do!" (for the present imperative).

As for sequence of tenses, the translators took care to follow English rules rather than Greek in translating Greek presents, imperfects and aorists. Thus, where English says, "We knew that he was doing," Greek puts it, "We knew that he does" similarly, "We knew that he had done" is the Greek, "We knew that he did." Likewise, the English, "When he had come, they met him," is represented in Greek by: "When he came, they met him." In all cases a consistent transfer has been made from the Greek tense in the subordinate clause to the appropriate tense in English.

In the rendering of negative questions introduced by the particle me (which always expects the answer "No") the wording has been altered from a mere, "Will he not do this?" to a more accurate, "He will not do this, will he?"

### EXPLANATION OF GENERAL FORMAT

NOTES AND CROSS REFERENCES are placed in a column adjoining the text on the page and listed under verse numbers to which they refer. Superior numbers refer to literal renderings, alternate translations, or explanations. Superior letters refer to cross references. Cross references in italics are parallel passages.

PARAGRAPHS are designated by bold face verse numbers or letters.

QUOTATION MARKS are used in the text in accordance with modern English usage.

"THOU," "THEE" AND "THY" are not used in this edition and have been rendered as "YOU" and "YOUR." [previous editions read, ". are not used in this translation except in the language of prayer when addressing Deity."]

PERSONAL PRONOUNS are capitalized when pertaining to Deity.

ITALICS are used in the text to indicate words which are not found in the original Hebrew, Aramaic, or Greek but implied by it. Italics are used in the marginal notes to signify alternate readings for the text. Roman text in the marginal alternate readings is the same as italics in the Bible text.

SMALL CAPS in the New Testament are used in the text to indicate Old Testament quotations or obvious references to Old Testament texts. Variations of Old Testament wording are found in New Testament citations depending on whether the New Testament writer translated from a Hebrew text, used existing Greek or Aramaic translations, or paraphrased the material. It should be noted that modern rules for the indication of direct quotation were not used in biblical times thus, the ancient writer would use exact quotations or references to quotation without specific indication of such. [previous editions read, ". not used in biblical times, thus allowing freedom for omissions or insertions without specific indication of these."]

A STAR (*) is used to mark verbs that are historical presents in the Greek which have been translated with an English past tense in order to conform to modern usage. The translators recognized that in some contexts the present tense seems more unexpected and unjustified to the English reader than a past tense would have been. But Greek authors frequently used the present tense for the sake of heightened vividness, thereby transporting their readers in imagination to the actual scene at the time of occurrence. However, the translators felt that it would be wise to change these historical presents to English past tenses.

[ ] = In text, brackets indicate words probably not in the original writings

## Preface

The New International Version is a completely new translation of the Holy Bible made by over a hundred scholars working directly from the best available Hebrew, Aramaic and Greek texts. It had its beginning in 1965 when, after several years of exploratory study by committees from the Christian Reformed Church and the National Association of Evangelicals, a group of scholars met at Palos Heights, Illinois, and concurred in the need for a new translation of the Bible in contemporary English. This group, though not made up of official church representatives, was transdenominational. Its conclusion was endorsed by a large number of leaders from the many denominations who met in Chicago in 1966.

Responsibility for the new version was delegated by the Palos Heights group to a self-governing body of fifteen, the Committee on Bible Translation, composed for the most part of Biblical scholars from colleges, universities and seminaries. In 1967 the New York Bible Society (now the International Bible Society) generously undertook the financial sponsorship of the project&mdasha sponsorship that made it possible to enlist the help of many distinguished scholars. The fact that participants from the United States, Great Britain, Canada, Australia and New Zealand worked together gave the project its international scope. That they were from many denominations&mdashincluding Anglican, Assemblies of God, Baptist, Brethren, Christian Reformed, Church of Christ, Evangelical Free, Lutheran, Mennonite, Methodist, Nazarene, Presbyterian, Wesleyan and other churches&mdashhelped to safeguard the translation from sectarian bias.

How it was made helps to give the New International Version its distinctiveness. The translation of each book was assigned to a group of scholars. Next, one of the Intermediate Editorial Committees revised the initial translation, with constant reference to the Hebrew, Aramaic or Greek. Their work then went to one of the General Editorial Committees, which checked it in detail and made another thorough revision. This revision in turn was carefully reviewed by the Committee on Bible Translation, which made further changes and then released the final version for publication. In this way the entire Bible underwent three revisions, during each of which the translation was examined for its faithfulness to the original languages and for its English style.

All this involved many thousands of hours of research and discussion regarding the meaning of the texts and the precise way of putting them into English. It may well be that no other translation has been made by a more thorough process of review and revision from committee to committee than this one.

From the beginning of the project, the Committee on Bible Translation held to certain goals for the New International Version: that it would be an accurate translation and one that would have clarity and literary quality and so prove suitable for public and private reading, teaching, preaching, memorizing and liturgical use. The Committee also sought to preserve some measure of continuity with the long tradition of translating Scriptures into English.

In working toward these goals, the translators were united in their commitment to the authority and infallibility of the Bible as God&rsquos Word in written form. They believe that it contains the divine answer to the deepest needs of humanity, that it sheds unique light on our path in a dark world, and that it sets forth the way to our eternal well-being.

The first concern of the translators has been the accuracy of the translation and its fidelity to the thought of the Biblical writers. They have weighed the significance of the lexical and grammatical details of the Hebrew, Aramaic, and Greek texts. At the same time, they have striven for more than a word-for-word translation. Because thought patterns and syntax differ from language to language, faithful communication of the meaning of the writers of the Bible demands frequent modifications in sentence structure and constant regard for the contextual meaning of words.

A sensitive feeling for style does not always accompany scholarship. Accordingly, the Committee on Bible Translation submitted the developing version to a number of stylistic consultants. Two of them read every book of both Old and New Testaments twice&mdashonce before and once after the last major revision&mdashand made invaluable suggestions. Samples of the translation were tested for clarity and ease of reading by various kinds of people&mdashyoung and old, highly educated and less well educated, ministers and laymen.

Concern for clear and natural English&mdashthat the New International Version should be idiomatic but not idiosyncratic, contemporary but not dated&mdashmotivated the translators and consultants. At the same time, they tried to reflect the differing styles of the Biblical writers. In view of the international use of English, the translators sought to avoid obvious Americanisms on the one hand and obvious Anglicisms on the other. A British edition reflects the comparatively few differences of significant idiom and spelling.

As for the traditional pronouns &ldquothou&rdquo and &ldquothine&rdquo in reference to the Deity, the translators judged that to use these archaisms (along with old verb forms such as &ldquodoest,&rdquo &ldquowouldest&rdquo and &ldquohadst&rdquo) would violate accuracy in translation. Neither Hebrew, Aramaic nor Greek uses special pronouns for the persons of the Godhead. A present translation is not enhanced by forms that in the time of the King James version were used in everyday speech, whether referring to God or man.

For the Old Testament the standard Hebrew text, the Masoretic Text as published in the latest editions of Biblia Hebraica, was used throughout. The Dead Sea Scrolls contain material bearing on an earlier stage of the Hebrew Text. They were consulted, as were the Samarian Pentateuch and the ancient scribal traditions relating to textual changes. Sometimes a variant Hebrew reading in the margin of the Masoretic text was followed instead of the text itself. Such instances, being variants within the Masoretic tradition, are not specified by footnotes. In rare cases, words in the consonantal text were divided differently from the way they appear in the Masoretic text. Footnotes indicate this. The translators also consulted the more important early versions&mdashthe Septuagint Aquila, Symmachus and Theodotion the Vulgate the Syriac Peshitta the Targums and for the Psalms the Juxta Hebraica of Jerome. Readings from these versions were occasionally followed where the Masoretic Text seemed doubtful and where accepted principles of textual criticism showed that one or more of these textual witnesses appeared to provide the correct reading. Such instances are footnoted. Sometimes vowel letters and vowel signs did not, in the judgment of the translators, represent the correct vowels for the original consonantal text. Accordingly some words were read with a different set of vowels. These instances are usually not indicated by footnotes.

The Greek text used in translating the New Testament was an eclectic one. No other piece of ancient literature has such an abundance of manuscript witnesses as does the New Testament. Where existing manuscripts differ, the translators made their choice of readings according to accepted principles of New Testament textual criticism. Footnotes call attention to places where there was uncertainty about what the original text was. The best current printed texts of the Greek New Testament were used.

There is a sense in which the work of translation is never wholly finished. This applies to all great literature and uniquely so to the Bible. In 1973 the New Testament in the New International Version was published. Since then, suggestions for corrections and revisions have been received from various sources. The Committee on Bible Translation carefully considered the suggestions and adopted a number of them. These were incorporated in the first printing of the entire Bible in 1978. Additional revisions were made by the Committee on Bible Translation in 1983 and appear in printings after that date.

As in other ancient documents, the precise meaning of the biblical texts is sometimes uncertain. This is more often the case with the Hebrew and Aramaic texts than with the Greek texts. Although archaeological and linguistic discoveries in this century aid in understanding difficult passages, some uncertainties remain. The more significant of these have been called to the reader&rsquos attention in the footnotes.

In regard to the divine name YHWH, commonly referred to as the Tetragrammaton, the translators adopted the device used in most English versions of rendering that name as &ldquo Lord &rdquo in capital letters to distinguish it from Adonai, another Hebrew word rendered &ldquoLord,&rdquo for which small letters are used. Wherever the two names stand together in the Old Testament as a compound name of God, they are rendered &ldquoSovereign Lord .&rdquo

Because for most readers today the phrase &ldquothe Lord of hosts&rdquo and &ldquoGod of hosts&rdquo have little meaning, this version renders them &ldquothe Lord Almighty&rdquo and &ldquoGod Almighty.&rdquo These renderings convey the sense of the Hebrew, namely, &ldquohe who is sovereign over all the &lsquohosts&rsquo (powers) in heaven and on earth, especially over the &lsquohosts&rsquo (armies) of Israel.&rdquo For readers unacquainted with Hebrew this does not make clear the distinction between Sabaoth (&ldquohosts&rdquo of &ldquoAlmighty&rdquo) and Shaddai (which can also be translated &ldquoAlmighty&rdquo), but the latter occurs infrequently and is always footnoted. When Adonai and YHWH Sabaoth occur together, they are rendered &ldquothe Lord, the Lord Almighty.&rdquo

As for other proper nouns, the familiar spellings of the King James Version are generally retained. Names traditionally spelled with &ldquoch,&rdquo except where it is final, are usually spelled in this translation with &ldquok&rdquo or &ldquoc,&rdquo since the biblical languages do not have the sound that &ldquoch&rdquo frequently indicates in English&mdashfor example, in chant. For well known names such as Zechariah, however, the traditional spelling has been retained. Variation in the spelling of names in the original languages has usually not been indicated. Where a person or place has two or more different names in the Hebrew, Aramaic or Greek text, the more familiar one has generally been used, with footnotes where needed.

To achieve clarity the translators sometimes supplied words not in the original texts but required by the context. If there was uncertainty about such material, it is enclosed in brackets. Also for the sake of clarity or style, nouns, including some proper nouns, are sometimes substituted for pronouns, and vice-versa. And though the Hebrew writers often shifted back and forth between first, second and third personal pronouns without change of antecedent, this translation often makes them uniform, in accordance with English style and without the use of footnotes.

Poetical passages are printed as poetry, that is, with the indentation of lines and separate stanzas. These are generally designed to reflect the structure of Hebrew poetry. This poetry is normally characterized by parallelism in balanced lines. Most of the poetry of the Bible is in the Old Testament, and scholars differ regarding the scansion of Hebrew lines. The translators determined the stanza divisions for the most part by analysis of the subject matter. The stanzas therefore serve as poetic paragraphs.

As an aid to the reader, italicized sectional headings are inserted in most of the books. They are not to be regarded as part of the NIV text, are not for oral reading, and are not intended to dictate the interpretation of the sections they head.

The footnotes in this version are of several kinds, most of which need no explanation. Those giving alternative translation begin with &ldquoOr&rdquo and generally introduce the alternative with the last word preceding it in the text, except when it is a single-word alternative in poetry quoted in a footnote a slant mark indicates a line division. Footnotes introduced by &ldquoOr&rdquo do not have uniform significance. In some cases two possible translations were considered to have about equal validity. In other cases, though the translators were convinced that the translation in the text was correct, they judged that another interpretation was possible and of sufficient importance to be represented in a footnote.

In the New Testament, footnotes that refer to uncertainty regarding the original text are introduced by &ldquoSome manuscripts&rdquo or similar expressions. In the Old Testament, evidence for the reading chosen is given first, and evidence for the alternative is added after a semicolon (for example: Septuagint Hebrew father). In such notes the term &ldquoHebrew&rdquo refers to the Masoretic text.

It should be noted that minerals, flora and fauna, architectural details, articles of clothing and jewelry, musical instruments and other articles cannot always be identified with precision. Also measures of capacity in the biblical period are particularly uncertain (see the table of weights and measures following the text).

Like all translations of the Bible, made as they are by imperfect man, this one undoubtedly falls short of its goals. Yet we are grateful to God for the extent to which he has enabled us to realize these goals and for the strength he has given us and our colleagues to complete our task. We offer this version of the Bible to him in whose name and for whose glory it has been made. We pray that it will lead many into a better understanding of the Holy Scriptures and a fuller knowledge of Jesus Christ the incarnate Word, of whom the Scriptures so faithfully testify.

## Definitions for preface ˈprɛf ɪs pref·ace

The beginning or introductory portion that comes before the main text of a document or book.

The book included a brief preface by a leading expert in the field.

To introduce or make a comment before the main point.

Let me preface this by saying that I don't know him that well.

The part of the liturgy that precedes the main part of the Eucharist

The book included a brief preface by a leading expert in the field.

### Webster Dictionary (0.00 / 0 votes) Rate this definition:

something spoken as introductory to a discourse, or written as introductory to a book or essay a proem an introduction, or series of preliminary remarks

the prelude or introduction to the canon of the Mass

to introduce by a preface to give a preface to as, to preface a book discourse

### Freebase (0.00 / 0 votes) Rate this definition:

A preface is an introduction to a book or other literary work written by the work's author. An introductory essay written by a different person is a foreword and precedes an author's preface. The preface often closes with acknowledgements of those who assisted in the literary work. A preface generally covers the story of how the book came into being, or how the idea for the book was developed this is often followed by thanks and acknowledgments to people who were helpful to the author during the time of writing. A preface is usually signed a foreword by another person is always signed. Information essential to the main text is generally placed in a set of explanatory notes, or perhaps in an "Introduction" that may be paginated with Arabic numerals, rather than in the preface. The term preface can also mean any preliminary or introductory statement. It is sometimes abbreviated pref. Preface comes from the Latin, meaning either "spoken before" or "made before". While the former source of the word could have preface meaning the same as prologue, the latter strongly implies an introduction written before the body of the book. With this meaning of stated intention, British publishing up to at least the middle of the twentieth century distinguished between preface and introduction.

## Finally:

The above are some of the points that one must keep in mind while writing the preface of the project work. You need to work in a professional manner and if you are willing to put your best into the project, then certainly you will want to initiate the project with the professional attitude only.

The preface is something which can decide whether the reader is interested in the project or no like if the preface is not saying anything, maybe the reader drops the idea for further reading of the project.