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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
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accepted The number of $n$-tuples with a sum less than $m$ is $C_m^n$?
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asked The number of $n$-tuples with a sum less than $m$ is $C_m^n$?
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accepted You only need countable many sets each time in a generated $\sigma$-algebra, right?
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accepted How do I prove that $\cos{\frac{2\pi}{7}}\notin\mathbb{Q}$?
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accepted Why is this unbounded linear functional also has a closed kernel?
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accepted If a linear functional is not bounded, then it has a non-closed kernel.