Mathematical Proof
Maths: Edexcel A Level Pure Maths, topic 1.3.1
What is Mathematical Proof?
A proof is a mathematical argument that explicitly shows that a given statement is always true.
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.
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.
How do you write numbers in proofs?
- If we know that a number is even, we can rewrite it as , where is an integer.
- If we know that a number is odd, we can rewrite it as , where is an integer.
- Consecutive numbers are written as
Test yourself on Mathematical Proof
A conjecture is said to be true for all positive integers .
Which of the following assumptions is true?
A conjecture is said to be true for all integers .
Which of the following assumptions is true?
If an integer is divisible by 10, how else can we write it?