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Jan
11
comment Random solving of a Rubik cube .
@TonyK Actually, that's equivalent to what I already said. We also need the fact that the number of states is finite.
Jan
11
comment Random solving of a Rubik cube .
@TonyK It was merely an argument to make it unlikely that it's infinite. I think we'll also need the fact that each state only needs a finite number of moves in order to be solved?
Jan
11
comment Random solving of a Rubik cube .
Why would it be infinite? From every state of the cube, there is a nonzero chance that you will only apply the best move from that point on until the cube is solved.
Sep
21
revised proving $n!>2^n\;\;\forall \;n≥4\;$ by mathematical induction
improved formatting
Aug
17
accepted Power tower inequality
Jun
25
awarded  Yearling
Dec
15
awarded  Caucus
Dec
15
comment Combinatorics in a Party.
Exactly. I agree with @drhab and I think OP misunderstood the question.
Nov
19
comment Differentiability of a function on $\mathbb R$ such that $f(x+1)=f(x)$.
I bet you meant "Finally, (c) is clearly false."?
Nov
5
revised Inequality proof by induction, what to do next in the step
corrected spelling
Nov
5
comment Inequality proof by induction, what to do next in the step
It's not extremely easy to see that $$2\left(\sqrt{n+2}-\sqrt{n+1}\right) = \frac{2}{\sqrt{n+2}+\sqrt{n+1}},$$ though.
Nov
5
answered Inequality proof by induction, what to do next in the step
Sep
30
awarded  Explainer
Jul
2
awarded  Curious
Jun
25
awarded  Yearling
Feb
3
awarded  Good Answer
Nov
20
revised Prove that $ \sum_{1 \le t \le n, \ (t, n) = 1} t = \dfrac {n\phi(n)}{2} $
Removed \displaystyle in the title.
Nov
20
suggested approved edit on Prove that $ \sum_{1 \le t \le n, \ (t, n) = 1} t = \dfrac {n\phi(n)}{2} $
Oct
19
comment Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism.
Hint: use \left( and \right) for larger brackets when using exponents.
Oct
19
answered There are 10 different people at a party. How many ways are there to pair them off into a collection of five pairings?