Archives for Physics, Math - Page 3
pigeonhole principle problem solving
Suppose 82 students are enrolled in a college – offering only 4 courses. Suppose that each course has 3 sections – and a student can choose any one of three…
Remove a countable set of points from an open set
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…
Single Event Probabilities
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…
Joint Event Probabilities
See also ‘Single Event Probabilities’ The probability of a 'joint' event - drawing a white ball followed by two black balls (from a jar containing 7 white and 5 black…
Open sets and limit points
A set $A$ is open iff for every point $a\in A$, there exists a $\delta$ such that the neighborhood $\left(a-\delta,a+\delta\right)$ surrounding $a$ is completely contained within (is a subset of)…
What about accelerating frames of reference?
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 ; She still feels…
centripetal versus centrifugal force
Centrifugal force is observed by the rotating bucket of water – pulling it towards the ; The bucket of water is in a noninertial frame ,what we (in our own…
Comparing temperatures in centigradeS
Is 20 C twice as hot as 10 C? No - because the centigrade scale does not start at if we used a meter scale that started at meters, what…
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 –…
Prove that there are a countable number of intervals (in R) with rational endpoints
Counting Elements versus Counting Intervals The interval is one interval, is another and so on. Start with one end-point Just count the left end points of . Now for a…