Let A be an open set. Show that if a finite number of points are removed from A, the remaining set is still open. Is the same true if a countable number of points are removed? Solution If we order the points removed from A, x1...

# Category - Math

Number theory, complex variables (applications), fourier analysis and applications.

Binomial Random Variable – and Probability of SINGLE event happening more than once (multiple heads in a coin-toss etc.) Whenever you have a variable that can take on two possible values (flip of a coin for example), you...

See also ‘Single Event Probabilities’ The probability of a ‘joint’ event – e.g. drawing a white ball followed by two black balls (from a jar containing 7 white and 5 black balls) can be calculated using...

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 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...

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...

How often have you stared at a math problem, unsure of where to begin? The thing is, most math books cover the basic lemmas and theorems – but provide little instruction on the TYPES of problems those lemmas can help with. So...

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...

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...

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...