G. Paseman
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Why is compactness in logic called compactness?
8 votes

A motto which is related (and sometimes true) is "proofs are finite". In most systems of logic under consideration, the statement and a proof of the statement are finite strings of symbols. One can ...

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Prove: $(a + b)^{n} \geq a^{n} + b^{n}$
5 votes

Here is another way to look at the inequality. Pick the larger of $a^n$ and $b^n$ and divide through by that quantity. This reduces the problem to showing that $(1+r)^n \ge 1 + r^n$ for some ...

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Surprising Generalizations
4 votes

Galois connections are further reaching than one first realizes. One small application is in model theory, where the relation R between sentences of a theory and models given by t R M if sentence t ...

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Degree sequence of a graph has repeated entries
3 votes

If there were no repeats, what would the degree sequence look like? Why could it not look like that?

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Number of ways to partition a rectangle into n sub-rectangles
3 votes

Here is a non-answer which may prove interesting and tractable. Given a configuration of rectangles that properly tile a surrounding rectangle, one can represent the tiling in a number of ways. Two ...

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Sum of two periodic functions
2 votes

If each function has a smallest period, and otherwise fits the conditions, then a proof may be forthcoming by attempting to compute the smallest period of the sum and failing. However, things become ...

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Bertrand's Postulate
Accepted answer
2 votes

Three related points are worthy of mention, showing that epsilon can be close to n. There is a result of Finsler that approximates how many primes lie between n and 2n, which is of order o(n/log(n)) ...

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How do I measure distance on a globe?
2 votes

If you have the Euclidean distance d between the two points, and set D = the diameter of the sphere (so D = 2R), then the great circle distance is D*InvSin(d/D), where InvSin is the inverse sine ...

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Mean of highest exponent in prime factorization of all integers ≥ 2
Accepted answer
1 votes

Here are some suggestions to approximate the limit. Consider F(n) to be the greater of 1 and the highest power of 2 that appears in the prime factorization of n. Show what the limit of the average ...

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Least wasteful use of stamps to achieve a given postage
1 votes

A similar problem is known in mathematics. It is called the "Postage-Stamp" problem, and usually asks which postal values can be realized and which cannot. Dynamic programming is a common but not ...

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Counting placing items in bins according to boolean restrictions
1 votes

This is an example of a Constraint Satisfaction Problem. If you have more objects than bins, you can sometimes treat the bins individually (as a poster did with the case of one bin) and multiply the ...

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Calculate the remainder when there are division
Accepted answer
1 votes

This sounds similar to computing the last nonzero base-10 digit of factorial(n). The fact that you are, according to some scheme, dropping the last bit of what would otherwise be a Fibonacci sequence ...

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Is there a direct proof of this lcm identity?
0 votes

It will need something clever. For $n + 1 = 6$, you need $6$ times the lcm of $1, 5$ and $10$ in order to get enough powers of 2 ( and 3 ). Is there a characterization of those $n + 1$ where the ...

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A high school competition-level problem concerning sum and sequence
0 votes

Determining a nice form for $A(n)$ is a good start. This is $S(n) - S(n-1) = 2n + 2 $. Now the desired sum is \begin{equation*} \sum_{k= 1}^{10} A(2k-1) = \sum_{k=1}^{10} 4k = 4 \ast 10 \ast 11 / 2 ...

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