Free taster
5 of 6 sections open
Proving It's ALWAYS True
Proving It's ALWAYS True
"The sum of two consecutive numbers is always odd." Is this true? You could try 5 + 6 = 11 ✓, or 100 + 101 = 201 ✓. But that doesn't PROVE it's always true. With algebra, n + (n+1) = 2n + 1, which is always odd!
What is a counter-example in mathematics?: A single specific example that shows a statement is NOT always true.
One counter-example is enough to disprove a conjecture.
Mathematics glossary
- What is a counter-example in mathematics?
- A single specific example that shows a statement is NOT always true. One counter-example is enough to disprove a conjecture.
Now try it yourself
Quiz · Question 1 of 14
Which expression represents an even number for all integer values of n?
Tap an answer to check it
This topic in real past papers
Every real exam question we've found on proof, with a full worked answer.
AQA Paper 1
Three of the four sittings we have full papers for use a given identity or a comparison of coefficients, always testing whether the identity is applied rather than just recognised.
Edexcel Paper 1
Two of the three sittings we have full papers for ask for a full proof, once about odd and even integers and once about the areas of semicircles on a right-angled triangle.