1.3.1

Mathematical Proof

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What is Mathematical Proof?

A proof is a mathematical argument that explicitly shows that a given statement is always true.

Illustrative background for What is the difference between a theorem and a conjecture?Illustrative background for What is the difference between a theorem and a conjecture? ?? "content

What is the difference between a theorem and a conjecture?

  • A theorem is a mathematical statement that has been proven to always be true.
  • A conjecture is a mathematical statement that has not been proven to always be true yet.
  • You will be asked to prove that a given conjecture is true.
Illustrative background for What are assumptions in proofs?Illustrative background for What are assumptions in proofs? ?? "content

What are assumptions in proofs?

  • Assumptions are the conditions under which the conjecture is true.
  • For example, a common assumption is that a conjecture holds for all positive integers.
    • If we know a number is a positive integer, then its square must also be a positive integer.
    • We can then use this fact as a step in a proof.
Illustrative background for How do you write numbers in proofs?Illustrative background for How do you write numbers in proofs? ?? "content

How do you write numbers in proofs?

  • If we know that a number is even, we can rewrite it as 2n2n, where nn is an integer.
  • If we know that a number is odd, we can rewrite it as 2n+12n+1, where nn is an integer.
  • Consecutive numbers are written as n,n+1,n+2,...n, n+1,n+2,...

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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