Xiv Contents 56 Linear Extensions 461 Sorting 465 Linear Extensions of Infinite Posets 467 Recap 468 Exercises 468 57 Dimension 469 Realizers 469 Dimension 471 Embedding 473 Recap 476 Exercises 476 58 Lattices 477 Meet and Join 477 Lattices 479 Recap 481 Exercises 482 Chapter 10 Self Test 483 Appendices 487 A Lots of Hints and Comments;Some Answers 487 B Solutions to Self Tests 515 Chapter 1 515 Chapter 2 516 Chapter 3 518 Chapter 4 520 Chapter 5 524 Chapter 6 526 Chapter 7 530 Chapter 8 532 Chapter 9 535 Chapter 10 539 C Glossary 544 D Fundamentals 552 Numbers 552 Operations 552 Ordering 553 Complex Numbers 553 Substitution 553 Index 555xiv Contents 56 Linear Extensions 461 Sorting 465 Linear Extensions of Infinite Posets 467 Recap 468 Exercises 468 57 Dimension 469 Realizers 469 Dimension 4 71 Embedding 473 Recap 476 Exercises 4 7 6 58 Lattices 477 Meet and Join 4 77 Lattices 4 79 Recap 481 Exercises 482 Chapter 10 Self Test 483 Appendices 487 A Lots of Hints and Comments; Some Answers 487 8 Solutions to Self Tests 515 Chapter 1 515 Chapter 2 516 Chapter 3 518 Chapter 4 520 Chapter 5 524 Chapter 6 526 Chapter 7 530 Chapter 8 532 Chapter 9 535 Chapter 10 539 c Glossary 544 D Fundamentals 552 Numbers 552 Operations 552 Ordering 553 Complex Numbers 553 Substitution 553 Index 555