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Apr
11
awarded  Popular Question
Mar
30
comment The number of $n$-tuples with a sum less than $m$ is $C_m^n$?
You are absolutely right. How did I miss that? By the way @Solomon's answer is equivalent. The key point is summing.
Mar
30
accepted The number of $n$-tuples with a sum less than $m$ is $C_m^n$?
Mar
30
asked The number of $n$-tuples with a sum less than $m$ is $C_m^n$?
Mar
23
awarded  Popular Question
Mar
11
awarded  Yearling
Dec
10
accepted You only need countable many sets each time in a generated $\sigma$-algebra, right?
Nov
5
accepted How do I prove that $\cos{\frac{2\pi}{7}}\notin\mathbb{Q}$?
Jul
11
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Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
30
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Jun
2
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Mar
11
awarded  Yearling
Feb
19
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Dec
16
accepted Why is this unbounded linear functional also has a closed kernel?
Dec
15
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Dec
11
accepted If a linear functional is not bounded, then it has a non-closed kernel.
Dec
11
comment If a linear functional is not bounded, then it has a non-closed kernel.
Oh, I get it. It's because according to one of the definitions of unbounded linear operator, there exists $y_n$, with $\|y_n\|=1$ but $|f(y_n)|\to\infty$, now let $x_n=y_n/|f(y_n)|$ and we get what we want.
Dec
11
comment If a linear functional is not bounded, then it has a non-closed kernel.
Why is $V/\ker f$ a finite dimensional space?