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Jan
23
comment Is it true that, for accumulation points, $(A \cup B)' \subset A' \cup B'$?
It might be a good idea to state that the notation $C'$ means the derived set of $C$. I first took it to mean the complement of $C$, and thought the whole problem was crazy.
Jan
23
comment probability that 3rd head occurred on 9th trial
There were 2 heads in the first 8 trials; the 9th trial was a head; the 10th and 11th trails were tails. Analyzing it that way, can you work out the probability?
Jan
23
comment Calculating the number of states in power of 10's
Let's start with a simpler problem. Suppose you have 17 bits. How many possible states are there?
Jan
23
comment How do we deal with recurrence relation characteristic equations that are not quadratic or have imaginary roots?
Absence of evidence is not evidence of absence. In any event, solving the recurrence may mean finding a formula for $H(n)$, in which case after you've seen it's $a,b,b-a,-a,-b,a-b$ repeating you still have to find a formula for it (which I know you can do, Will, but maybe not everyone can).
Jan
23
comment How do we deal with recurrence relation characteristic equations that are not quadratic or have imaginary roots?
Approximating the sequence is a bit harder than what you've written, if there's a repeated root and/or a tie for root of largest magnitude.
Jan
23
comment How do we deal with recurrence relation characteristic equations that are not quadratic or have imaginary roots?
Even generating functions pose problems in degrees three and up.
Jan
23
answered Help with evaluating an integral
Jan
23
answered Exhibit a cycle with a power having a given cycle shape
Jan
23
comment $\binom{n}{n+1} = 0$, right?
Except for the part about $(-1)!=0$ --- I don't see where that comes from, and it's not the usual convention.
Jan
23
comment Probability, coin flip
Right. Now can you go on to do the original question?
Jan
23
comment Find two points across diameter a circle, based on a known position and an isosceles triangle produced from these three points.
@vonbrand, who said anything about tangents? OP is looking for two points "across the diameter of the circle," so we are not talking about tangents here (unless OP is very confused about what the problem is).
Jan
23
comment Probability, coin flip
Why are you assuming something, when it is possible to calculate it? The probability the 1st person gets exactly three heads is not $(1/2)^3$. This is where you have to start.
Jan
23
comment “Multiplying” by a dt then cancelling?
"Cancelling the $dt$" is a notational convenience, not a genuine cancellation of anything. And, please, for future reference, you drive people crazy when you have to edit the question several times before you finally get it right. Try to take the time and care to get it right on the first go.
Jan
23
answered How do we deal with recurrence relation characteristic equations that are not quadratic or have imaginary roots?
Jan
23
comment Probability, coin flip
Do you know how to calculate, for example, the probability that they both get exactly three heads? Do you know how to calculate the probability that, say, the 1st person gets exactly three heads?
Jan
23
comment Probability, coin flip
hibc, the notation you use is not as important as the concepts you understand. Ross is telling you that you have to compute a bunch of probabilities, multiply them in pairs, and then add up the products. Do you understand each step of that? If not, ask Ross to clarify whichever step you don't get.
Jan
23
comment “Multiplying” by a dt then cancelling?
The third equation is a nonsense. Don't worry about it, someone just got careless.
Jan
23
comment Powers of a greatest common denominator
Did you notice that your friend Bill had already posted an answer to the question I flagged as a duplicate?
Jan
23
revised Find the maximum value of product given the sum
formatting
Jan
23
comment Find the maximum value of product given the sum
Prove that if two of the summands differ by more than $1$ then you can increase the product by making those two summands closer to each other.