Tag Archives: Proof

Universal and Existential Quantifiers example (x<y)

Posted on January 14, 2022 by Sumant Sumant
Posted in Logic, Proof | Tagged | Leave a comment

Geometric Proof of Irrationality of Sqrt(2)

Posted on November 12, 2019 by Sumant Sumant
Posted in Geometry, Number Theory, Proof, Proof by Contradiction, Real Analysis, Trick | Tagged , , | 1 Comment

2^(1/n) is irrational for n > 2

Posted on August 12, 2015 by Sumant Sumant

Theorem: is irrational for Let us assume that  which by fermat’s last theorem is impossible 🙂

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Divisible numbers among 2n numbers when n+1 are chosen

Posted on January 3, 2015 by Sumant Sumant

Prove that if you choose numbers out of numbers then there will be two numbers one of which divides the other. We observe that there are even numbers and also odd numbers. Now any number between and can be written … Continue reading →

Posted in Pegion Hole, Prime Numbers, Proof | Tagged , | Leave a comment

e versus pi expoenents

Posted on January 2, 2015 by Sumant Sumant

Which is bigger or To answer this first take a look at the power series of . Now if then . We notice that  or . Therefore choosing we get . Polya used this idea to prove AM-GM inequality So we can … Continue reading →

Posted in Inequalities, Proof | Tagged , , , , , , , | Leave a comment

Cauchy Schwartz Inequality

Posted on January 1, 2015 by Sumant Sumant

One of the most famous inequality in Math is Cauchy-Schwartz inequality. The easiest case is . To prove it all one has to do is simplify: crossmultiplying  we get From this one can get the formula . To prove it … Continue reading →

Posted in Inequalities, Proof | Tagged , , | Leave a comment