Answer all the questions below and press submit to see how many you got right.
Assumption : An assumption is something that we assume to be true as part of trying to prove a statement. Assumptions play a critical role in proofs by induction and proof by contradiction.
Contradiction : A contradiction is a statement that is the opposite of one of the assumptions. As not both a statement and its opposite can be true at the same time this forms the basis of proofs by contradiction.
Finite : Finite means not infinite. For example the number of solutions of $x^2=1$ is finite but the number of solutions of $\sin x=0$ is infinite.
Infinity : Infinity or $\infty$ represents a number that is bigger than all numbers in $\mathbb{R}.$
Number : A number $x$ is a mathematical symbol representing a quantity.
Prime number : A prime number is a natural number bigger than 1 that only has 1 and itself as a factor. The first five prime numbers are 2, 3, 5, 7 and 11. There is an infinite number of prime numbers.
Proof : A proof is a logical deduction of a result starting only with the assumptions of the result.
We want to prove by contradiction that there is an infinite number of prime numbers. What is a good assumption at the start of the proof?
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