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1d
comment Limit of Sum $\sum \frac{p(k+1) - p(k)}{p(k)^2}$ ? (corrected)
Agree that convergence follows from known results about prime gaps. The number $\frac{1}{2}$ for the sum, or any nice number, would be miraculous.
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reviewed Reopen How to find the second derivative of an implicit function?
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answered Question about proof with geometric sums
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answered To prove the sum is convergent
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revised Total number of unique n-element sets from a base of unique elements
added 423 characters in body
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comment Total number of unique n-element sets from a base of unique elements
I will add the calculation in the answer, since writing math in comments is more awkward.
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comment Can $x^x$ be a natural number for non-integer $x$?
Yes, if $p/q$ we take the $q$-th power.
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comment Is there no propositional letter in first order logic?
Because they are not needed.
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comment Is there no propositional letter in first order logic?
Some people include True and False, which are atomic formulas. All the logic books I have used leave them out in the presentation of first-order logic.
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comment Can $x^x$ be a natural number for non-integer $x$?
It cannot be a non-integer rational.
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comment Is there no propositional letter in first order logic?
You are welcome. There are propositional symbols because without them, the language would be empty.
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comment Can $x^x$ be a natural number for non-integer $x$?
You are welcome. Your question, as mentioned by triple_sec, is settled by Gelfond-Schneider.
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answered Can $x^x$ be a natural number for non-integer $x$?
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answered Is there no propositional letter in first order logic?
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revised Total number of unique n-element sets from a base of unique elements
added 226 characters in body
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answered Total number of unique n-element sets from a base of unique elements
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comment Is this an error? (An Introduction to the Theory of Computation by Eitan Gurari)
I have not taken a good enough look at it to judge. Last taught a course like that quite a few years ago, am no longer familiar with the newer textboos.
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revised Is this an error? (An Introduction to the Theory of Computation by Eitan Gurari)
added 90 characters in body
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answered Is this an error? (An Introduction to the Theory of Computation by Eitan Gurari)
2d
comment A Question about the Proof of Eisenstein's Irreducibity Criterion
The proof should start with "Let us assume that $f(x)$ is not irreducible." Under that assumption, $f(x)$ is the product of two non-trivial polynomials with integer coefficients. The constant terms of both cannot be divisible by $p$, but the constant term of one must be.