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.
Irrational number : An irrational number is a real number that can not be written as a fraction. $\sqrt{2}$ and $\pi$ are examples of irrational numbers.
Proof : A proof is a logical deduction of a result starting only with the assumptions of the result.
Rational number : A rational number is a number of the form $\frac{a}{b}$ with integers $a, b.$
Square root of 2 : The square root of 2 also written as $\sqrt{2}$ is the positive number such that $(\sqrt{2})^2=\sqrt{2}\cdot \sqrt{2}=2.$ $\sqrt{2}$ is an irrational number and rounded to the nearest hundredths it is equal to 1.41.
We want to prove by contradiction that $\sqrt{2}$ is irrational. What is a good assumption at the start of the proof?
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