Kirjahaku

The first of series of 5 books, this book tells the history of life on Earth from the planet's formation 4,550 million years ago until the end of the Paleozoic Era 252 million years ago. In this beautiful full-color illustrated book, you will learn about: How life began in the seas as simple single-celled organismsHow single-celled organisms grew more complex and changed the planetThe sudden appearance of many multicellular life forms during the Cambrian explosionHow life colonized the landThe evolution of the first tetrapods (four-limbed vertebrates) from fishHow tetrapods diversified to produce reptiles and our ancestors, the synapsid mammal-like reptilesThe greatest mass extinction in history that brought the Paleozoic Era to a closeAnd much more Table of Contents: Introduction Chapter 1: How the Earth was FormedThe Formation of the Solar SystemThe Formation of the Planets Including Earth. Chapter 2: The Hadean EonConditions in the Hadean Eon Chapter 3: The Archean EonConditions in the Archean EonProkaryota - The First Life Chapter 4: Proterozoic EonThe Great Oxygenation Event and the Huronian GlaciationMore Complex Life - EukaryotaThe Cryogenian PeriodThe Ediacaran Period - The First Multicellular Life Chapter 5: The Phanerozoic Eon and the Paleozoic EraEras of the Phanerozoic EonPeriods of the Paleozoic Era Chapter 6: The Cambrian PeriodPaleogeography of the Cambrian PeriodThe Cambrian ExplosionAnimals of the Cambrian PeriodPlants of the Cambrian PeriodMass Extinctions of the Cambrian Period Chapter 7: The Ordovician PeriodPaleogeography of the Ordovician PeriodClimate of Ordovician PeriodThe Ordovician RadiationAnimals of the Ordovician PeriodMass Extinctions of the Ordovician Period Chapter 8: The Silurian PeriodPaleogeography of the Silurian PeriodClimate of Silurian PeriodAnimals of the Silurian PeriodLife on Land Chapter 9: The Devonian PeriodPaleogeography of the Devonian PeriodMarine Life in the Devonian PeriodThe First TetrapodsThe Devonian ExplosionMass Extinctions of the Devonian Period Chapter 10: The Carboniferous Period (including Mississippian and Pennsylvanian Subperiods)Paleogeography of the Carboniferous PeriodClimate of Carboniferous PeriodForests and Coal DepositsMarine Life in the Carboniferous PeriodAmphibians of the Carboniferous PeriodThe First AmniotesTerrestrial Arthropods of the CarboniferousThe Carboniferous Rainforest CollapseThe Diversification of Amniotes - Parareptiles, Synapsids and Diapsids Chapter 11: The Permian PeriodPaleogeography of the Permian PeriodClimate of the Permian PeriodPlants of the Permian PeriodAmphibians of the Permian PeriodParareptiles of the Permian PeriodDiapsids of the Permian PeriodSynapsids of the Permian PeriodInsects of the Permian PeriodMass Extinctions of the Permian Period Chapter 12: The Mesozoic and Cenozoic ErasThe Mesozoic EraThe Cenozoic Era

This book provides a complete guide to scientific notation (known in the UK as standard form) and engineering notation. It explains how the notation works, the advantages of using it, how to convert to and from it, how to compare numbers and orders of magnitude, and even how to perform approximate arithmetic operations (without using a calculator) such as addition, subtraction, multiplication, division, exponentiation, square roots, cube roots, and logarithms on numbers in scientific notation. There are over 200 questions and answers (answers explain how to get the answer) to help you master this important math topic. Table of contents is: Chapter 1: What are Scientific Notation and Engineering Notation?Whole Number Powers of 10What is Scientific Notation?- Converting Decimal Numbers to Normalized Scientific Notation- Converting Scientific Notation to DecimalWhat is Normalized Scientific Notation (Standard Form)?- Significant Figures- Estimated Final Digits- E-notation and Other Notational Standards- Converting Decimal Numbers to Normalized Scientific Notation- Converting Scientific Notation to DecimalWhat is Engineering Notation?- Significant Figures- Engineering Notation and SI Unit Prefixes- Converting Decimal Numbers to Engineering Notation- Converting Engineering Notation to DecimalNormalizing and Denormalizing Numbers in Scientific and Engineering Notation- Increasing the Value of the Exponent and Decreasing the Absolute Value of the Coefficient- Decreasing the Value of the Exponent and Increasing the Absolute Value of the Coefficient- Converting a Number in Normalized Scientific Notation to Engineering Notation- Converting a Number in Engineering Notation to Normalized Scientific NotationQuestions Answers to Chapter 1 Questions Chapter 2: Comparing Numbers in Scientific NotationComparing Numbers in Normalized Scientific NotationComparing Numbers in Engineering NotationComparing Numbers in Denormalized Scientific NotationQuestions Answers to Chapter 2 Questions Chapter 3: Orders of MagnitudeDefinitions of Order of MagnitudeOrder of Magnitude EstimatesOrder of Magnitude Differences- Approximate Order of Magnitude Differences Questions Answers to Chapter 3 Questions Chapter 4: Adding & SubtractionHow to Add Numbers in Scientific and Engineering Notation- Approximate Addition in Scientific and Engineering NotationHow to Subtract Numbers in Scientific and Engineering Notation- Approximate Subtraction in Scientific and Engineering NotationQuestions Answers to Chapter 4 Questions Chapter 5: Multiplication and DivisionHow to Multiply Numbers in Scientific and Engineering Notation- Approximate Multiplication in Scientific and Engineering NotationHow to Divide Numbers in Scientific and Engineering Notation- Approximate Division in Scientific and Engineering NotationQuestions Answers to Chapter 5 Questions Chapter 6: ExponentiationHow to Exponentiate Numbers in Scientific and Engineering Notation- Approximate Exponentation in Scientific and Engineering NotationHow to Find Approximate Square Roots in Scientific and Engineering NotationHow to Find Approximate Cube Roots in Scientific and Engineering NotationQuestions Answers to Chapter 6 Questions Chapter 7: LogarithmsHow to Calculate Approximate Logarithms in Base 10How to Calculate Approximate Logarithms in Base 2How to Calculate Approximate Natural LogarithmsQuestions Answers to Chapter 7 Questions Conclusion

I was fat, I was unfit, and I was over 40. At my maximum, I probably weighed around 252 pounds (114 kg), but the truth is I am not really sure. Today, I am close to my ideal weight at just 182 pounds (83kg), fitter than I have probably ever been, regularly play competitive sport, and have completed several extremely demanding physical challenges. This book is the story of how I did it, and how I believe you can too Part personal story, part guidebook, inside you will find a "no holds barred" account of exactly how I permanently changed my lifestyle so eating healthily and doing regular exercise became not only routine, but easy. This book isn't a diet or exercise plan, doesn't tell you precisely what to eat, or how to work-out, but it does contain a detailed roadmap to how you can change your life for the better, and watch the weight fall away. Some of things you will discover include: How to consistently measure your weight so as to make it easy to do day-to-day comparisons How to keep track of your weight, and really know if you are gaining or losing How to set yourself weight loss goals, and adjust them as you go How to make healthy lifestyle choices that you will stick with rather than abandon after a short time The most reliable way to incorporate regular exercise into your daily routine How to choose sporting activities that will keep you motivated How setting ambitious goals can help you achieve more than you might have ever thought possible How to shop for healthy foods, and how to really read labels Simple adjustments to the types of food you eat that can save on calories and help you lose weight Suggestions for reducing the calorie counts in your breakfast, lunch, and dinner How to deal with snacking (including 11 low-calorie snack suggestions) Tips to help you eat more healthily when eating out Ideas for boosting your metabolism, and even to help you burn more calories when on vacation at the beach In short, if you want to lose weight, have tried diet and exercise plans, and they either haven't worked for you, or you've been unable to stick with them - then this book is for you. These ideas worked for me - and they can work for you too

This book is a complete introduction to learning, understanding, and mastering working with fractions (sometimes known as "common fractions", "simple fractions", or "vulgar fractions"), and is based on the author's personal experience providing 1:1 mathematics tuition to both school students and adult numeracy students. Topics covered include: What is a fractionNames of fractionsFractions as division (converting a fraction into a division calculation and back)Mixed numbersImproper ("top heavy") fractionsConverting mixed numbers to top heavy fractionsConverting whole numbers to top heavy fractionsConverting top heavy fractions to mixed numbersEquivalent fractionsSimplifying fractionsExpressing fractions in their simplest formComparing fractionsAdding fractions (including adding several fractions together)Subtracting fractionsMultiplying fractions (including multiplying several fractions together)Simplifying fraction multiplicationsDividing fractionsSimplifying complex fractions (fractions within a fraction)How to convert fractions into decimal numbersHow to convert decimal numbers into fractionsEvery topic is explained in detail, complete with many step-by-step worked examples and diagrams. Additionally. major topics are immediately followed by a set of practice questions (there are well over 300 questions in total in the book), the answers to which can be found at the end of each chapter. In summary, whether you want to learn fractions yourself, or teach your kids fractions, or are a student preparing for exams such as GCSEs or high school maths tests, or are an adult learner wishing to improve your numeracy and knowledge of this important math topic - this book is ideal for you.

Knowing multiplication tables is a key math skill. This is because multiplication tables are not only directly useful, but are also a foundation upon which other mathematical techniques are based - including multiplication of larger numbers, division, and fractions. This book is a guide for parents wishing to help their kids master this important skill. It shows parents how to teach their kids in a simple step-by-step fashion, and includes numerous tips and tricks to help children remember, or work out, the answers. Times tables from 0X0 to 12X12 are covered, and as well as the times tables themselves, the book also includes additional facts, such as common prefixes used for words relating to various numbers, how to quickly check if a number is in the 2, 3, 4, 5, 6, 9, or 10 times table, and more.

This book is a guide to the 5 Platonic solids (regular tetrahedron, cube, regular octahedron, regular dodecahedron, and regular icosahedron). These solids are important in mathematics, in nature, and are the only 5 convex regular polyhedra that exist. Topics covered include: What the Platonic solids are The history of the discovery of Platonic solids The common features of all Platonic solids The geometrical details of each Platonic solid Examples of where each type of Platonic solid occurs in nature How we know there are only five types of Platonic solid (geometric proof) A topological proof that there are only five types of Platonic solid What are dual polyhedrons What is the dual polyhedron for each of the Platonic solids The relationships between each Platonic solid and its dual polyhedron How to calculate angles in Platonic solids using trigonometric formulae The relationship between spheres and Platonic solids How to calculate the surface area of a Platonic solid How to calculate the volume of a Platonic solid Also included is a brief introduction to some other interesting types of polyhedra - prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra. Some familiarity with basic trigonometry and very basic algebra (high school level) will allow you to get the most out of this book - but in order to make this book accessible to as many people as possible, it does include a brief recap on some necessary basic concepts from trigonometry.

This book is a complete introduction to repeating decimals (also known as "recurring decimals"), including how to convert repeating decimals into fractions, and is based on the author's personal experience providing 1:1 mathematics tuition to both school students and adult numeracy students. Topics covered include: What is a terminating decimal What is a repeating decimal Different types of repeating decimal notation (including common US and UK notations) The disadvantages of using ellipses to represent repeating decimal numbers Converting between the different types of repeating decimal notation Identifying the reptend of repeating decimals Understanding spoken-English descriptions of repeating decimals The problems with common spoken-English ways of pronouncing repeating decimals How to unambiguously state repeating decimal values in spoken-English Rational numbers are numbers that can be expressed as fractions All rational numbers are terminating or repeating decimals Irrational numbers are numbers that can not be expressed as fractions All irrational numbers are non-terminating non-repeating decimals Converting a fraction into its equivalent terminating or repeating decimal Why all fractions must convert into either terminating decimals or repeating decimals Which fractions convert into terminating decimals and which into repeating decimals How to convert repeating decimals into their equivalent fractions Every topic is explained in detail, complete with many step-by-step worked examples. Additionally. major topics are immediately followed by a set of practice questions, the answers to which can be found at the end of each chapter.

Radians are the preferred unit that mathematicians and scientists use for measuring angles. Likewise steradians are the preferred unit used for measuring solid angles. This book explains the key concepts behind radians and steradians, as well as how to perform mathematical calculations based on these units (including many worked examples, questions for you to do yourself, and answers to those questions to check your results). Topics covered in the book include: Key terminology associated with circlesA comparison between measuring angles in degrees and other units such as gradiansThe definition of radians How angles can be measured in radiansWhy radians are a "natural" unit for measuring anglesHow many radians correspond to a full circle rotation, half circle rotation, and a quarter circle rotation (right angle)How many degrees correspond to a radianHow to convert degrees into radiansHow to convert radians into degreesConversions of some common angles between degrees and exact radian valuesHow to calculate arc lengths using radiansHow to calculate sector perimeters using radiansHow to calculate sector areas using radiansHow to calculate chord lengths using radiansHow to calculate segment perimeters using radiansHow to calculate major and minor segment areas using radiansRadians usage as an SI UnitSome uses of radians in physicsCommon SI Unit prefixes of radians, and subject areas where you may encounter themMilliradian approximations used in various militaries and in gunneryDimensional analysis involving radiansThe definition of steradiansHow many steradians are in a complete sphere and in a hemisphereHow to calculate the aperture angle of a cone of 1 steradianSome common applications of steradiansDimensional analysis involving steradians

Exponentiation, raising a number to a power, is usually the next mathematical operation that students learn about after mastering addition, subtraction, multiplication and division. This book is principally about exponentiation and performing mathematical operations on expressions that involve exponents. Additionally, the book introduces surds such as square roots, and explains how to perform common mathematical operations involving such surds. In this book, among other things, you will learn: How exponents are pronouncedThe meanings of the words base, exponent, index (plural: indices), and exponentiation How to multiply numbers and algebraic symbols with exponentsHow to divide numbers and algebraic symbols with exponentsHow to raise numbers and algebraic symbols with exponents to a powerHow multiplications and divisions involving different base numbers with exponents can sometimes be simplifiedHow to solve problems with fractional exponentsWhat are surdsHow to perform arithmetic on expressions that contain surdsHow to simplify surds and expressions containing surdsHow to expand brackets when surds are involvedHow to simplify fractions containing surds including "rationalizing the denominator"

This book introduces the binary, octal and hexadecimal numbering systems used in computer science and computer programming. It introduces how numbers are represented in each of these systems, how to convert between them (and to and from base 10). In this book, among other things, you will learn: What are number bases (also known as radixes)What is binary (base 2) How to convert binary numbers to denary (base 10)How to convert denary numbers to binaryWhat is octal (base 8)How to convert octal numbers to denaryHow to convert denary numbers to octalWhy many programmers and computer scientists use octal How to convert octal numbers to binaryHow to convert binary numbers to octalWhat is hexadecimal (base 16)How to convert hexadecimal numbers to denaryHow to convert denary numbers to hexadecimalWhy many programmers and computer scientists use hexadecimal How to convert hexadecimal numbers to binaryHow to convert binary numbers to hexadecimalIs there a reason to prefer octal over hexadecimal or vice-versa?

This book explains how the binary works & how it is used by computers to represent information including positive & negative integers, characters & real numbers. It explains the logical & bitwise operations used to manipulate information & perform arithmetic. We also briefly look at how computers store this information in memory & secondary storage, & how it can be transmitted between computers. Topics covered include: INTRODUCING NUMBER BASES & BINARY CONVERTING FROM BINARY TO DENARY & VICE-VERSAHow to Convert a Binary Number to DenaryHow to Convert a Denary Number to Binary HOW COMPUTERS GROUP BINARY DIGITSA Closer Look at BytesA Closer Look at Words-Word alignment, word alignment & packing, byte ordering & endiannessAddresses BOOLEAN OPERATIONS & LOGIC GATESFundamentals of Boolean Algebra-NOT, AND, OR, XOR, NAND, NOR, NXORCombining Logic Gates-NOT, AND, OR, XOR, NOR using NAND logicLogical Versus Bitwise OperationsUsing Bitwise Operations to Set, Clear, Flip or Test Bits-Setting bits, inverting bits, clearing bits, testing bits ADDING & SUBTRACTING IN BINARYAdding Binary Integers-The column addition method of adding denary numbers & adding binary numbers, implementing binary addition using logic gatesSubtracting Binary Integers-The column subtraction methods of subtracting denary numbers & subtracting binary numbers, implementing binary subtraction using logic gates SHIFT OPERATIONSLeft ShiftRight ShiftCircular Shifts MULTIPLICATION & DIVISION IN BINARYMultiplication-Multiplying by a power of 2, column multiplication, Russian peasant multiplication algorithm, multiplication in hardwareDivision-Dividing by a power of 2, denary long division, binary long division, algorithm for binary long division, division in hardware REPRESENTING CHARACTERS & STRINGS OF CHARACTERSRepresenting Individual Characters-ASCII, extended ASCIIs, BCDIC & other early character encodings, EBCDIC, UnicodeRepresenting Strings of Characters-Terminated strings, length-prefixed strings, other string representations REPRESENTING TEXT & GRAPHICS ON SCREENd104 Mode DisplaysBitmap Displays PARITY CHECKINGWhat is a Parity BitEven & Odd ParityAdvantages, Disadvantages & Limitations of Using Parity CheckingParity's Use in RAID Storage DevicesUnused Parity Bits SIGNED INTEGERSOffset BinarySigned Magnitude RepresentationOne's ComplementTwo's ComplementOther Representations of Signed Numbers-Base -2, signed-digit representation REAL NUMBERSFixed Point RepresentationFloating Point RepresentationRational Data TypeLogarithmic Number Systems DENARY ENCODINGS & DECIMAL DATA TYPESWhy Use Denary Representations of Real Numbers?Binary Encodings of Denary-Serial decimal, two-out-of-five, bi-quinary, character-based encodings of denary, binary-Coded Decimal (BCD), Chen-Ho Encoding, Densely Packed Decimal (DPD) & excess-3Decimal Data Types-Which numbers can be exactly represented in fixed & floating point?-How inexact?-Issues with inexact representation-Decimal representation DATA STRUCTURESStructsArraysLinked Lists & More Complex Structures-Limitations of arrays, introducing linked lists, singly & doubly linked lists, more complex data structures TYPES OF COMPUTER MEMORYMagnetic-Core Memory & Core Rope MemoryRAM-DRAM & SRAMROM-Mask-programmed ROM, PROM, EPROM, EEPROM, Flash memory SECONDARY STORAGESequential Storage-Punched tape, magnetic tapeRandom Access Storage-Magnetic disk, optical disk, solid state drives, flash memory & cloud storage MEASURING MEMORY & STORAGE DIGITAL COMMUNICATIONSSerial CommunicationParallel Communication MEASURING TRANSFER RATESBaud

Have hours of fun with over 100 word search puzzles. Find words hidden in any direction: left to right, right to left, upwards, downwards or in any diagonal direction. Find 20 to 30 target words per puzzle. All puzzles are unique to this book and have never been published before.

This book is a step-by-step guide for introducing your child to addition. Simple and easy steps and colorful pictures will help you teach this important math skill. Before you know it, they will be able to add two, three or four numbers together, and be ready to move on to the next stage: column addition.

The grid method (also known as the box method) is the way that most children today learn to multiply large numbers. It can seem baffling to parents who learnt traditional long multiplication - but this step-by-step guide solves that problem Colorful examples, and questions and answers (100 in total) will help you and your children master the grid method in next to no time.

A comprehensive guide to performing mole and stoichiometric calculations with numerous examples, as well as questions and answers. Covers calculations relating to solids, solutions, gases and electrolysis, plus as limiting and excess reactants, chemical yields, atom economy and much more. Fully up to date with the last international standards - including the revised definition of mole which was agreed on November 16th, 2018.

A detailed guide to arithmetic sequences (also known as arithmetic progressions), including how to identify them, how to find the terms, creating formulae to describe the terms of an arithmetic sequences, calculating the sum and mean of an sequence, and more. Easy-to-follow step-by-step explanations, numerous examples, and 80 questions and answers - including showing you to solve each question and reach the answer. Topics include: INTRODUCING ARITHMETIC SEQUENCESWhat is a Sequence?What is an Arithmetic Sequence?Checking if a Sequence is an Arithmetic SequenceFinding the Common Difference of an Arithmetic Sequence from Adjacent TermsFinding the Common Difference of an Arithmetic Sequence from Non-Adjacent TermsFinding the Next Terms in an Arithmetic SequenceFinding the Previous Terms in an Arithmetic SequenceFinding Missing Terms in an Arithmetic Sequence FINDING AND USING THE FORMULA FOR A PARTICULAR ARITHMETIC SEQUENCEFinding the FormulaUsing the Formula to Find a Particular TermUsing the Formula to Check Whether and Where a Particular Term is in a SequenceUsing the Formula to Find the First Term Greater Than a Target ValueUsing the Formula to Find the First Term Less Than a Target Value A GENERAL FORMULA FOR THE TERMS IN AN ARITHMETIC SEQUENCECreating the FormulaUsing the FormulaFinding the Values of a and d CALCULATING THE SUM AND MEAN OF AN ARITHMETIC SEQUENCEGauss at Elementary SchoolGenerating a Formula for the Sum of Arithmetic SequenceUsing the Sum FormulaFinding the Sum of Ranges of Terms within an Arithmetic SequenceGenerating a Formula for the Arithmetic Mean of an Arithmetic SequenceSimultaneous Equations Involving the Sum and/or Mean

A complete guide to the Solar System including the Sun, all the planets, all the recognised dwarf planets & much else besides - major moons, asteroids, comets, meteoroids & more. You'll also learn about the what lies beyond the Solar System, how the Solar System was formed & how it is expected to evolve in future. Contains numerous color pictures, illustrations & diagrams that will fascinate amateur astronomers & junior scientists. Updated April 2020 Table of Contents: 1: The Solar System: A Whistle-Stop TourThe SunThe Planets-How Many Planets?-How Far are the Planets from the Sun?-Planetary Orbits-Planetary Rotation-Types of PlanetsMinor Planets, Dwarf Planets & Comets-Minor Planets of the Inner Solar System - Asteroids-Minor Planets of the Outer Solar System-Dwarf Planets-CometsMeteoroids, Micrometeoroids & Space Dust-Meteors & Meteorites-Sources of Meteoroids & Micrometeoroids-Meteor Showers & Meteor StormsMoons-How Many Moons are There?-Can a Moon Have Its Own Moons?-How Big Can Moons Be?-How Small Can Moons Be?-Orbital Characteristics of Moons-Tidal Locking-Trojan Satellites 2: The SunName & DiscoveryPhysical CharacteristicsRotationStudy & Exploration 3: MercuryName & DiscoveryPhysical CharacteristicsOrbitRotationMoonsStudy & ExplorationLife? 4: VenusName & DiscoveryPhysical CharacteristicsOrbitRotationMoonsStudy & ExplorationLife? 5: EarthName & DiscoveryPhysical CharacteristicsStudy & ExplorationOrbitRotationThe MoonStudy & ExplorationLife 6: MarsName & DiscoveryPhysical CharacteristicsOrbitRotationMoonsStudy & ExplorationLife? 7: JupiterName & DiscoveryPhysical CharacteristicsOrbitRotationRingsMoonsStudy & ExplorationLife? 8: SaturnName & DiscoveryPhysical CharacteristicsOrbitRotationRingsMoonsStudy & ExplorationLife? 9: UranusName & DiscoveryPhysical CharacteristicsOrbitRotationRingsMoonsStudy & ExplorationLife? 10: NeptuneName & DiscoveryPhysical CharacteristicsOrbitRotationRingsMoonsStudy & ExplorationLife? 11: Planet NineName & DiscoveryPhysical CharacteristicsOrbitRotationRingsMoonsStudy & ExplorationLife? 12: CeresName & DiscoveryPhysical CharacteristicsOrbitRotationStudy & ExplorationLife? 13: PlutoName & DiscoveryPhysical CharacteristicsOrbitRotationMoonsStudy & ExplorationLife? 14: HaumeaName & DiscoveryPhysical CharacteristicsOrbitRotationRingMoonsStudy & ExplorationLife? 15: MakemakeName & DiscoveryPhysical CharacteristicsOrbitRotationMoonsStudy & ExplorationLife? 16: ErisName & DiscoveryPhysical CharacteristicsOrbitRotationMoonsStudy & ExplorationLife? 17: Beyond the Solar SystemStars-Types of Stars-Distances to Stars-Other Solar SystemsGalaxies-Types of Galaxies-Our Galaxy - The Milky WayGroups, Clusters & Superclusters 18: The History of the Solar SystemThe Big BangThe First StarsLater StarsThe Birth of the Solar SystemThe Formation of the Planets & Asteroids-Terrestrial Planets-Giant Planets-The Asteroid Belt-Planetary MigrationMoonsLate Heavy Bombardment 19: The Future of the Solar SystemThe SunThe PlanetsMoonsThe Milky Way & the Local GroupThe Ultimate Fate of the Universe Conclusion