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  • 0 posts edited
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  • 32 votes cast
Jul
6
comment Prove that $V$ is the direct sum of $W_1, W_2 ,\dots , W_k$ if and only if $\dim(V) = \sum_{i=1}^k \dim W_i$
I think you mean the sum of the dimension of the span of $B_i $ is the dimension of $W_i $.
Jul
4
comment Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$.
My question would be if this proof is correct. I saw this problem in an old analysis book and so I thought I would try it out. Sorry, I should have been more clear.
Jul
4
revised Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$.
added 148 characters in body
Jul
4
comment Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$.
Sorry about that, I have corrected the statement in my edit.
Jul
4
revised Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$.
added 98 characters in body
Jul
4
asked Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$.
Jun
19
accepted If, $\lim x_n$ exists and finite then there is a function $f$ that is continuous
Jun
19
asked If, $\lim x_n$ exists and finite then there is a function $f$ that is continuous
Jun
6
accepted Difficult limits every grad should be able to do
Jun
5
asked Difficult limits every grad should be able to do
May
27
accepted $\lim_{n\to \infty} n^{1/n^2}$
May
27
comment $\lim_{n\to \infty} n^{1/n^2}$
Ahh, this is much better. Thanks!
May
27
asked $\lim_{n\to \infty} n^{1/n^2}$
May
26
comment Bounded sequence of positive numbers
Do you mean $r $ instead of $K $?
May
26
accepted Bounded sequence of positive numbers
May
26
asked Bounded sequence of positive numbers
May
19
accepted Residue Theorem and Homologous to zero
Apr
14
accepted Improper Integral with trigonometric functions
Apr
14
comment Improper Integral with trigonometric functions
Well this integral diverges so my integral will diverge by the comparison test. Correct?
Apr
14
asked Improper Integral with trigonometric functions