IB Maths AA 1.11 Definitions

This page contains our IB Maths AA definitions for 1.11. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Additional proofs'.

All Topic 1 Sub-topics 1.1: Scientific Notation 1.2: Arithmetic Sequences 1.3: Geometric Sequences 1.4: Interest 1.5: Exponents & Logs 1.6: Deductive Proofs 1.7: Binomial Theorem (HL)1.8: Counting principles (HL)1.9: Partial fractions (HL)1.10: Complex numbers (HL)1.11: Additional proofs (HL)1.12: Systems of equations

base

The initial value of

n

for which a claim is first verified in an induction argument, commonly

n=1

contradiction

An impossibility or inconsistency reached in an argument, such as deducing two statements that cannot both be true.

counterexample

A single example that makes a universal claim fail, showing the statement is not always true.

Induction hypothesis

The assumption that

P(k)

is true for some fixed

k\in\mathbb{N}

, used as a step in proving

P(k+1)

Inductive step

The part of an induction proof where, using the induction hypothesis,

P(k+1)

is proved to follow from

P(k)

opposite

The side that lies across from the chosen acute angle in a right-angled triangle.

proof

A sequence of logically valid steps showing that a statement is true.

Proof by contradiction

A method where the opposite of the desired statement is assumed and then logical consequences are derived until an impossibility or inconsistency is reached, forcing the original statement to be true.

Proof by mathematical induction

A method for proving a statement

P(n)

for all relevant positive integers by verifying an initial case and then showing that

P(k)

implies

P(k+1)

for some

k\in\mathbb{N}

universal

Describing a claim that applies to every element in a set, typically signalled by words such as “all”, “every”, “always”, or “no”.

Next Up

You have completed the topic 1 definitions for IB Maths AA - continue with related resources below or explore the full IB Maths AA course from the IBO.

Explored IB Maths AA Definitions?

Get stuck into one of our other subjects!

Other subjects' Definitions

Biology

Chemistry

Physics

Maths AI

Join 85,000 students, across 130+ countries, in 500+ IB schools. That's half of the IB science graduates worldwide.

Start a 7d free trial