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21h
answered a basic question about the natural Density
23h
comment Does a colouring of a graph on two colours always have certain kinda of circle
Does "circle contains no other points from $P$" mean that no other points of $P$ lie on the circle" or does it mean that no other points of $P$ lie inside the circle?
1d
answered Can a Set Have Infinitely-Many Non-Homeomorphic Topologies?
1d
answered How to find sum of $n$ terms of $3C_1+7C_2+11C_3+\cdots$
1d
awarded  Yearling
2d
revised How many permutations given some condition(s)
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2d
comment How many permutations given some condition(s)
@lightsout Have you had the inclusion-exclusion principle? Would you like to see a solution to part a using that?
Nov
22
revised Express $\cos \left ( 5x \right )$ via powers of $\sin \left ( x \right )$ and $\cos \left ( x \right )$?
added 1 character in body; edited title
Nov
22
answered symmetric difference
Nov
22
answered How many permutations given some condition(s)
Nov
22
comment At Most Two Distinct Members of A
In your question you claim that the displayed formula says something about A, but there is no A in the formula. Perhaps you have in mind some unstated connection between the set A and the predicate symbol P in the formula.
Nov
22
comment Find all such functions $f:R\to R$
Putting $y=1$ in $f(y)=(y/f(1))^4$ we get $f(1)^5=1$, so $f(1)=1$ since $f$ is assumed to be real-valued. Could there be complex-valued solutions?
Nov
22
comment Find all such functions $f:R\to R$
@PedroArbizu Putting $x=1$ in $f(yf(x))=x^2y^4$, we get $f(yf(1))=y^4$. If $f(1)=0$ this would mean $f(0)=y^4$ for all $y$, so $y^4$ is a constant, which is absurd; so $f(1)\ne0$. Replace $y$ with $y/f(1)$ in $f(yf(1))=y^4$.
Nov
22
comment Drawing balls one at a time without replacement.
It may be easier to figure the probability of not getting two consecutive balls of the same color, which you can then subtract from $1$. So, what's the probability of drawing all six balls with colors alternating between red and yellow? What's the probability for five balls?
Nov
22
comment What is $\Gamma(a)$?
This notation is defined in the paragraph at the top of p. 4.
Nov
22
revised Is every continuous one-to-one image of $[0,\infty)$ locally compact?
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Nov
22
revised Is every continuous one-to-one image of $[0,\infty)$ locally compact?
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Nov
22
answered Is every continuous one-to-one image of $[0,\infty)$ locally compact?
Nov
22
comment Repeated application of interesting function on tuples
What is CIMC???
Nov
22
comment At Most Two Distinct Members of A
Where do you get "P is a property that defines A"? There is nothing like that in the question.