Revision NotesExam QuestionsFlashcards
IBMathsDPAnalysis & Approaches (AA)HLFlashcards1. Number & AlgebraSimple Proof & Reasoning

Simple Proof & Reasoning (DP IB Analysis & Approaches (AA))

Flashcards

1/14

0Still learning

Know0

  • FrontProof

    What is proof in mathematics?

Enjoying Flashcards?
Tell us what you think

Cards in this collection (14)

  • What is proof in mathematics?

    Proof in mathematics is the use of a series of logical steps to show that a mathematical result is true for all specified cases.

    E.g. showing that the square of an odd number is odd for every odd number.

  • True or False?

    Seeing that a result works for a few numbers is enough to show it will work for all numbers.

    False.

    Seeing that a result works for a few numbers is not enough to show it will work for all numbers.

    A valid proof is required to show that it works for all values.

  • What symbol is used to denote the set of all integers?

    The set of all integers is denoted by the symbol straight integer numbers.

  • What symbol is used to denote the set of all positive integers?

    The set of all positive integers (1, 2, 3, ...) is denoted by the symbol straight integer numbers to the power of plus.

  • What is straight natural numbers the symbol for?

    The symbol straight natural numbers denotes the set of all natural numbers (0, 1, 2, 3, ...).

  • What is straight rational numbers the symbol for?

    straight rational numbers is the symbol for the set of all rational numbers.

    I.e., the set of all numbers that can be written in the form a over b, where a and b are integers and b not equal to 0.

  • Define the term mathematical identity.

    A mathematical identity is a statement that is true for all possible values of any variables used (for example x or theta).

  • What symbol is used to denote a mathematical identity?

    A mathematical identity is denoted by the symbol identical to.

  • What is proof by deduction?

    A proof by deduction uses known facts, and logical steps and arguments connecting those facts, to show that a mathematical result is true.

  • What algebraic convention is used to represent even numbers in proofs?

    In proofs, even numbers are typically represented as 2 n, where n is an integer.

    (2 k or 2 m are also often used in this way.)

  • What algebraic convention is used to represent odd numbers in proofs?

    In proofs, odd numbers are typically represented as 2 n minus 1, where n is an integer.

    2 n plus 1 may also be used.

    (Variables k or m are also often used instead of n in this context.)

  • What is proof by exhaustion?

    Proof by exhaustion is a way of proving a result by showing that the desired result works for every allowed value.

    This is a good method when there are only a limited number of cases or allowed values to check.

  • What is disproof by counter-example?

    Disproof by counter-example is a way of proving that a result is not true, by finding a case or value that does not work in the result.

    That case or value is called a counter-example

  • True or False?

    To disprove a result by counter-example, you need to show that the result does not work for every possible case or value.

    False.

    To disprove a result by counter-example, you only need to show that the result does not work for one particular case or value.

Previous:Sequences & SeriesNext:Proof by Induction & Contradiction

    1. Topic 1

      Number & Algebra Toolkit

    2. Topic 2

      Exponentials & Logs

    3. Topic 3

      Sequences & Series

    4. Topic 4

      Simple Proof & Reasoning

    5. Topic 5

      Proof by Induction & Contradiction

    6. Topic 6

      Binomial Theorem

    7. Topic 7

      Permutations & Combinations

    8. Topic 8

      Complex Numbers

    9. Topic 9

      Further Complex Numbers

    10. Topic 10

      Systems of Linear Equations

    1. Topic 1

      Linear Functions & Graphs

    2. Topic 2

      Quadratic Functions & Graphs

    3. Topic 3

      Functions Toolkit

    4. Topic 4

      Other Functions & Graphs

    5. Topic 5

      Reciprocal & Rational Functions

    6. Topic 6

      Transformations of Graphs

    7. Topic 7

      Polynomial Functions

    8. Topic 8

      Inequalities

    9. Topic 9

      Modulus Functions & Further Transformations

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Geometry of 3D Shapes

    3. Topic 3

      Trigonometry

    4. Topic 4

      The Unit Circle & Exact Values

    5. Topic 5

      Trigonometric Functions & Graphs

    6. Topic 6

      Trigonometric Equations & Identities

    7. Topic 7

      Inverse & Reciprocal Trigonometric Functions

    8. Topic 8

      Trigonometric Proof & Equation Strategies

    9. Topic 9

      Vector Properties

    10. Topic 10

      Vector Equations of Lines

    11. Topic 11

      Vector Planes

    1. Topic 1

      Statistics Toolkit

    2. Topic 2

      Correlation & Regression

    3. Topic 3

      Probability

    4. Topic 4

      Discrete Random Variables

    5. Topic 5

      Binomial Distribution

    6. Topic 6

      Normal Distribution

    7. Topic 7

      Continuous Random Variables

    1. Topic 1

      Differentiation

    2. Topic 2

      Techniques & Applications of Differentiation

    3. Topic 3

      Integration

    4. Topic 4

      Techniques & Applications of Integration

    5. Topic 5

      Optimisation

    6. Topic 6

      Kinematics

    7. Topic 7

      Basic Limits & Continuity

    8. Topic 8

      Further Differentiation

    9. Topic 9

      Further Integration

    10. Topic 10

      Differential Equations

    11. Topic 11

      Maclaurin Series

    12. Topic 12

      Limits using l'Hôpital's Rule & Maclaurin Series