Proof by Contradiction: Odd and Its Square

We have had several examples on proof by contradiction in this blog like irrationality of square root of 3 and the sum of root of 2 and root of 3. In this post, we will have another detailed example. In proof by contradiction, we want to change the statement “if P then Q” to “if NOT Q then […]
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Tangent Theorem 2

In the previous post on tangent theorem, we have learned that if a line is perpendicular to a radius of a circle at a point on the circle, then the line is tangent to the circle. In this post, we prove the converse of this statement. We prove that if a line is tangent to a […]
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Proof by Contradiction: 0.999… = 1

In the previous post, we proved that both by direct and indirect proof. The proof that we have used in the previous post was proof by contradiction. In proof by contradiction, we show that by assuming the proposition to false would imply a contradiction.  One of the most famous of this proof is the proof […]
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