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4 votes

Picking random natural number

No. Suppose $p(2) =1/1000$. Then $p(x) \gt 1/1000$ for $x=3,4,5,...,1003$. But those probabilities would then add up to more than $1.0$, which is impossible for probabilities. You should be able to ...
JonathanZ's user avatar
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2 votes

Rank of binary matrices: {0, 1} vs {-1, 1}

If you work over $\mathbf{Q}$ (or $\mathbf{R}$), which is the context in which that remark was made, there's a correspondence between $\{-1,1\}$ matrices and $\{0,1\}$ matrices with one less row and ...
Will Orrick's user avatar
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1 vote

Rank of binary matrices: {0, 1} vs {-1, 1}

Firstly, there is no relation between these two ranks. Your example shows rank$(M_{\{0,1\}})$ can be greater than rank$(M_{\{-1,1\}})$. Consider one matrix with all the entries equal to $0$ and one ...
ogirkar's user avatar
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