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Activity for Michael Hardy‭

Type On... Excerpt Status Date
Edit Post #296273 Post edited:
3 months ago
Edit Post #296273 Post edited:
3 months ago
Edit Post #296273 Post edited:
3 months ago
Comment Post #296264 @#117674 ok, Now I see what you meant by "set it off by line breaks."
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3 months ago
Comment Post #296264 It's working now, although nothing changed as far as I know.
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3 months ago
Edit Post #296262 Post edited:
3 months ago
Comment Post #296272 @#117674 I'm guessing that's accusative.
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3 months ago
Edit Post #284408 Post edited:
use of MathJax where appropriate
3 months ago
Edit Post #296273 Initial revision 3 months ago
Question "Weaker" versus "stronger" topologies
When I first learned point-set topology, the textbook said analysts and topologists have incompatible conventions about the meanings of "stronger" and "weaker" as applied to topologies. One of them means "finer" and the other "coarser," but which is which depends on whether you're an analyst or a...
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3 months ago
Edit Post #296272 Post edited:
3 months ago
Edit Post #296272 Initial revision 3 months ago
Answer A: What $\equiv$ called?
It depends upon the context. I am mainly posting to address a kind of confusion that often arises. There are two conventions of terminology and notation in modular arithmetic, and one should be clear about which is which. Newer notation: I suspect this one was introduced around the middle o...
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3 months ago
Suggested Edit Post #284408 Suggested edit:
use of MathJax where appropriate
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helpful 3 months ago
Edit Post #282060 Post edited:
The percent sign had the effect of commenting out the rest of the line, making an essential part of what was written invisible. It needs a backslash. Then it's legible. Also, use of \text{} where appropriate.
3 months ago
Edit Post #296266 Initial revision 3 months ago
Answer A: Can expectation be calculated if the events aren't numbered?
Putting letters instead of numbers on the six sides of a die does not change the codomain of the measure from $\mathbb R\cup\{\,+\infty,-\infty\,\}$ to something else. In fact, whether you use numbers or letters on the face of the die, the codomain of the measure is the set $[0,1]=\{\,x : 0\le x\...
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3 months ago
Edit Post #296262 Post edited:
3 months ago
Comment Post #296065 Are you sure it wasn't for use of the central limit theorem rather than for use of the z-test? (Either way, it's not really good advice.)
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3 months ago
Edit Post #296263 Post edited:
3 months ago
Comment Post #296264 I copied the code from this answer and pasted it into the question to which I linked. I don't know whether that changed anything or not, but it still doesn't work.
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3 months ago
Edit Post #296262 Post edited:
3 months ago
Edit Post #296262 Post edited:
3 months ago
Edit Post #296262 Post edited:
3 months ago
Comment Post #296155 Are you familiar with the usual meaning of the term "analytic continuation"?
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3 months ago
Edit Post #296262 Post edited:
3 months ago
Edit Post #296263 Initial revision 3 months ago
Question "align" in whatever software this site uses instead of MathJax
`\begin{align}` . . . `\end{align}`, a standard thing in LaTeX and in MathJax, does not work on this site, as seen in this answer. Can this be fixed?
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3 months ago
Edit Post #296262 Initial revision 3 months ago
Answer A: Can the relative magnitude of standardized coefficients indicate variable importance?
This can be hazardous if two predictors are correlated. For example, suppose one predictor is the amount of money a person spends on one kind of staple groceries and another is how much the same person spends on another kind of staple groceries. A person with a dozen dependents spends a lot on...
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3 months ago
Comment Post #296065 Why 30? Normally for estimating the mean of a normal (or "Gaussian") population, I would use a t-distibution until the sample size is at least 100 or so. I wonder whether you may be confusing this with the rough (and not very good) rule of thumb that says the sampling distribution of the sample m...
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3 months ago
Edit Post #296257 Post edited:
3 months ago
Edit Post #296257 Post edited:
3 months ago
Comment Post #296123 `\prod` is designed to be used in the way you used it in this question. In "inline" (as opposed to "displayed") contexts, the subscript on `\prod` is below and to the right of the symbol, unless that is manually overridden, as by the use of `\displaystyle`. But in a "displayed" context, it is dir...
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3 months ago
Comment Post #282060 Does $99\%$ accurate mean only $1\%$ positive among healthy people, or only $1\%$ negative among those who have the disease, or maybe both?
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3 months ago
Suggested Edit Post #282060 Suggested edit:
The percent sign had the effect of commenting out the rest of the line, making an essential part of what was written invisible. It needs a backslash. Then it's legible. Also, use of \text{} where appropriate.
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helpful 3 months ago
Edit Post #296257 Post undeleted 3 months ago
Edit Post #296257 Post edited:
3 months ago
Edit Post #296123 Post edited:
The code \mathcal{CB} was not between "dollar signs" and so not rendered. Using \prod rather than \Pi results in correct formatting of the subscript and other differences.
3 months ago
Comment Post #295614 There is no reason to think that the intersection of an open set in one topology and an open set in another topology must be empty.
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3 months ago
Edit Post #296257 Post deleted 3 months ago
Edit Post #296257 Post edited:
3 months ago
Edit Post #296257 Post edited:
3 months ago
Edit Post #296257 Post edited:
3 months ago
Edit Post #296257 Post edited:
3 months ago
Edit Post #296257 Initial revision 3 months ago
Answer A: Why is the union of two topologies not in general a topology?
Your last sentence makes me think you haven't understood your own question. There is no reason to think that the intersection of an open set in one topology and an open set in another must be empty. Consider the set $(0,1)\times(0,1).$ Let $\mathcal T1$ be the topology whose basic open sets ar...
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3 months ago
Comment Post #296123 Typing `\text{glb}` rather than `\operatorname{glb}` results in lack of proper spacing in things like $3\text{glb}S$ rather than $3\operatorname{glb}S$ (the latter coded as `3\operatorname{glb}S`). In a long document, you needn't type all of `\operatorname` every time since you can define a short...
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3 months ago
Suggested Edit Post #296123 Suggested edit:
The code \mathcal{CB} was not between "dollar signs" and so not rendered. Using \prod rather than \Pi results in correct formatting of the subscript and other differences.
(more)
helpful 3 months ago