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 - Physics, Math

Interesting Physics and Math Stuff

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...

If a woman is standing in an elevator, she feels a force of gravity pushing her against the floor. As the elevator accelerates upwards, this force increases. She still feels as if a ‘gravitational’ force has increased...

Centrifugal force is observed by the rotating bucket of water – pulling it towards the center. The bucket of water is in a noninertial frame ,what we (in our own inertial frame) observe is the centripetal...

Is 20 C twice as hot as 10 C? No – because the centigrade scale does not start at 0.For e.g.- if we used a meter scale that started at 1.0 meters, what can you say about comparing 1.1 to 1.2? Can you say that 1.2 is TWICE...

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...