1d
comment Open-Set Correspondence $\implies$ Continuity
It looks ok. You should mention your $n$-ball of radius $\delta$ has center $a$. This $n$-ball is the red disc. Your (otherwise nice) picture is mislabelled. The red disc is $B^{-1}$?)
1d
answered Normed space where unit ball's weak and norm topology coincide?
1d
comment Normed space where unit ball's weak and norm topology coincide?
This is of interest.
1d
comment The function is not continuous
What is $g$? Perhaps this is what you're after.
1d
comment Which of the following sets have the cardinality the same as $R$
For $Y$, a continuous function is determined by its values on the rationals.
1d
comment Is $ \text{Int} \overline{B(a;r)} = B(a;r)$ for a metric space $(X,d)$?
What about $(-1,1)\subset[-1,1]$?
1d
comment Logarithm problem
Had a typo at first; it's the correct formula now. Take logs of both sides of your equation and apply the above formula.
1d
comment Logarithm problem
$\log x^r=r\log x$.
1d
comment Riesz Lemma with $\alpha=1$ and Linear Bounded Functional
For the other direction, take $f\in X^*$, set $M={\rm ker}\, f$ and use this.
2d
comment That is My class work problem. but I don't understand how to calculate this problem. Can u help me?
$\pi\ne22/7$.${}$
2d
comment Q/ evaluate (d/dx)ln |tan x| .
Chain rule...${}$
2d
comment L'Hôpital's rule exercise with natural log function
Then what you did is perfectly correct.
2d
comment L'Hôpital's rule exercise with natural log function
Did you mean $\ln \bigl ((1/x)^x\bigr)$? (That's what I assumed above.)
2d
comment L'Hôpital's rule exercise with natural log function
$(1/x)^x$ tends to $1$; so its logarithm tends to zero.
2d
comment L'Hôpital's rule exercise with natural log function
$1$ is not the correct answer. Yours is.
May
19
comment Is this series computable?
This may give you some ideas.
May
19
revised Where does this result come in use?
added 14 characters in body; edited tags
May
18
comment An application of the uniform boundedness principle
See Problem 8 here for a solution using Baire category..
May
18
revised Prove that $f: [a,b] \rightarrow \mathbb{R}$ is strictly monotone
edited tags
May
17
comment uniform limit of step function
Hint: such an $f$ is uniformly continuous on the given interval.
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