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Apr
25
accepted If $f$ is increasing and continuous on $[a,b]$, then it is integrable there.
Apr
24
asked If $f$ is increasing and continuous on $[a,b]$, then it is integrable there.
Apr
23
accepted Permutation Group Notation
Apr
23
asked Permutation Group Notation
Apr
20
accepted Understanding a Property of the Riemann Integral
Apr
19
asked Understanding a Property of the Riemann Integral
Apr
19
accepted Equivalence of Two Different Irrational Numbers
Apr
19
comment If $x=[a_0;a_1,a_2,\dots]$, then $|x-C_k|<1/a_k^{\text{}}q_k^2$.
I also had the same feeling about this inequality. I will comment here again when I check whether this is a typo or not. Thanks!
Apr
19
accepted If $x=[a_0;a_1,a_2,\dots]$, then $|x-C_k|<1/a_k^{\text{}}q_k^2$.
Apr
18
answered Equivalence of Two Different Irrational Numbers
Apr
18
asked If $x=[a_0;a_1,a_2,\dots]$, then $|x-C_k|<1/a_k^{\text{}}q_k^2$.
Apr
18
comment Equivalence of Two Different Irrational Numbers
That makes a whole lot of sense! But I have one question: I suppose $\alpha$ and $\beta$ having different indexes ($a_j$ and $b_k$, respectively) does not really affect the induction step?
Apr
18
asked Equivalence of Two Different Irrational Numbers
Apr
18
accepted Equivalence of a Real Number to Itself
Apr
18
comment Equivalence of a Real Number to Itself
I cannot believe I just asked such a silly question... thanks.
Apr
18
asked Equivalence of a Real Number to Itself
Apr
18
accepted Continued Fractions Convergents $C_k-C_{k-3}$
Apr
18
asked Continued Fractions Convergents $C_k-C_{k-3}$
Apr
16
comment How to prove $n*\varphi(n)/2 $ sum?
I see it now. That makes perfect sense. Thanks. :) And +1 to the OP for this question.
Apr
16
comment How to prove $n*\varphi(n)/2 $ sum?
I fail to see how the equality follows from this. I know that $\sum_{1\leq k\leq n}k=\frac{n(n+1)}{2}$, but it seems that for this case, the $n+1$ term is replaced by $\varphi(n)$.