## Open sets and limit points

A set is open iff for every point , there exists a such that the neighborhood surrounding is completely contained within (is a subset of) . A point is a limit point of a set iff given any , all neighborhoods intersect the...

## The Monty hall problem, Quantum Games

The original problem Three doors, a prize behind only one door (say, a new car). Other two doors are each hiding a goat. Contestant has to pick a door – and hope that she wins the car.  At just this stage, the chance of...

## Prove that there are a countable number of intervals (in R) with rational endpoints

Counting Elements versus Counting Intervals  The interval [0,1) for example is uncountable, but we are not counting ELEMENTS of an interval, we are counting INTERVALS. [0,1] is one interval, [0,1/3] is another and so...

## Problem books for advanced math ( and physics ) students

How often have you stared at a math (or physics) problem, unsure of where to begin?  Most math books are unusually pedantic and dull – all in an attempt to be more ‘rigorous’. Screw rigor, I say.  Students are...

A Logical Paradox – The British Air Force Bombing Paradox The British Airforce announces that it will bomb the city sometime during this week; but at an unpredictable date. Why is this paradoxical. Suppose, they announce this...

## Income Inequality–GINI index

A number that ranges from 0 to 1 – to capture the Income inequality for a COUNTRY. By itself, the number means little, but in comparison with other countries, can convey much. A GINI index of 1 – would be if ONE family had...

## Write computer programs to learn physics and math

Where I grew up, we were taught math the hard way. We HAD to struggle through problems. No matter how complex or convoluted the problem was, it was almost a given that students would stay up – until they had solved it...

## Statistical Fallacies and Probability Teasers

Under construction Stock Trading – Incorrect Probability Conclusion Stock can either go up , down or stay still. Hence, probability of any one stock going down is 1/3 rd. Soldiers and Shell Bunkers – Incorrect...