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1d
comment Set theory intersections and unions
Incidentally, three of the regions of your current diagram are incorrectly filled. For example, one of them should say $0,$ as you determined. It's also worth noting that, when all $8$ regions are filled in, there will be no need to list the totals.
1d
comment Set theory intersections and unions
Just put "$28$" inside the rectangle, but outside all the circles.
1d
comment Set theory intersections and unions
And done! Nice work.
1d
comment Epsilon delta of recursively defined function
It might behoove you to rewrite the recursion term as $$a_{n+1}=\frac{a_n^2+5}{2a_n}.$$
1d
comment Set theory intersections and unions
Bingo! "Bonus points" if you can figure out how many students took only Latin, and how many students took only Sanskrit. That should let you fix and complete the Venn diagram (don't forget the exterior!) and check all your answers, as well as answer any other questions that might be asked about this situation.
1d
comment Set theory intersections and unions
Nicely done! So, you've concluded that $|L\cap S|=9.$ How does that let you answer the second question?
1d
comment Why is it possible to find the birth year by subtracting one's age from 114?
@user51189: Let me see if I can better explain Tyler's point. Suppose there is someone who was born on December 22nd, 1989. Today, then, they are 24, yes? But then the formula tells us that their birth year was 1990. Basically, the "formula" only works this year, and only works for people of certain ages (between 15 and 114) who have already had their birthday this year.
1d
revised Why is it possible to find the birth year by subtracting one's age from 114?
edited tags
1d
answered Set theory intersections and unions
1d
comment Find the fraction where the decimal expansion is infinite?
@MathisLife: I would be surprised if the decimal representation of the Fibonacci numbers were rational.
1d
comment Find the fraction where the decimal expansion is infinite?
Ah! Never mind. I missed the condition that the numerator and denominator must be less than $100.$
1d
comment proof of chain rule
Related.
Dec
18
comment Why doesn't it work when I calculate the second order derivative?
@longtemps: No you should not. $\frac{d^2y}{dx^2}$ is the second derivative of $y$ with respect to $x.$ It is not the second derivative of $y$ with respect to $x,$ divided by the square of the derivative of $x$ with respect to $t.$ Interpreting things that way is what got you the wrong answer from before!
Dec
18
comment The Island in the Miracle Sea. (Christmas edition)
@Jorge: The only issue I have with this formulation of the puzzle is that, for your solution to work, each elf on the island must know (or at least assume) that each other elf on the island is rational, which isn't made explicit. At any rate, +1!
Dec
18
answered If $x \in P$ and $x \neq 1$, then $x = S(y)$ for some $y \in P$
Dec
17
comment Is $\gamma(t) = (|t|,t)$ plot $y = x$?
(+1) Nice job! Another way to go is simply to note that $x$ cannot take on negative values, and so the plot is not of any non-vertical line. (In fact, not of any line at all, but that's enough for these purposes.)
Dec
17
comment Probability of ultimate extinction? Need to show that an infinite series is less than $1$
(+1) Oops! I managed to conflate the two. (Dinner time.)
Dec
17
revised Proving limit through definition
added 719 characters in body
Dec
17
answered Proving limit through definition
Dec
17
comment Probability of ultimate extinction? Need to show that an infinite series is less than $1$
You seem to have miscomputed your derivative. $$G_n'(s)=\sum_{r=1}^\infty \frac{n^{r-1}}{(n+1)^{r+1}}\frac{d}{dx}\left[s^r\right]= \sum_{r=1}^\infty\frac{rn^{r-1}}{(n+1)^{r+1}}s^{r-1}.$$