Monthly Archives: February 2017

At least one of 3 consecutive odd numbers is a multiple of 3

Posted on February 21, 2017 by Sumant Sumant

The first example is all these are primes but beyond that if there are three consecutive odds one of them will always be a prime. Let three consecutive odd numbers be . If is a multiple of then we are … Continue reading →

Posted in Number Theory | Leave a comment

Variance of Uniform Normal Distribution

Posted on February 21, 2017 by Sumant Sumant

Let the corresponding probabilities are for all at the points The general formula is Let’s first calculate Now lets calculate Therefore Now suppose we have same terms shifted from to in that case the variance becomes

Posted in Probability | Leave a comment

Archimedean Principle

Posted on February 13, 2017 by Sumant Sumant

There are 4 equivalent ways to express Archimedean Principle 1. If then there exists an such that . 2. The set of Positive Integers (Natural Numbers) is unbounded. For all natural numbers 3. If then there exists an such that … Continue reading →

Posted in Real Analysis | Leave a comment

Controlling distance with Triangle Inequality

Posted on February 6, 2017 by Sumant Sumant
Posted in Real Analysis | Leave a comment

Completeness Axiom and its significance

Posted on February 6, 2017 by Sumant Sumant

The general statement is: Any subset of real numbers that is bounded above has a supremum. Now this property is not shared by other number systems. We need the following to do calculus and we ask the question what makes … Continue reading →

Posted in Real Analysis | Leave a comment