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8h
revised Why can commuting matrices be simultaneously upper-triangularized?
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9h
comment Convergent of integral of $1/x^x$
How to format mathematics on this site
9h
revised Convergent of integral of $1/x^x$
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9h
reviewed Approve Convergent of integral of $1/x^x$
1d
comment How long will it take me to learn calculus?
You can certainly learn high school calculus in 3–6 weeks if you're bright, have good support, and work hard. I know this because I did it when I was your age and I know many other people who did it at the same age.
May
27
awarded  Favorite Question
May
27
comment In formal languages, why is $L^0 = \{ \epsilon \}$? Why isn't it the empty set ∅?
$0^0=1$ also, and the analogy for languages is that $\emptyset^0 = \{\epsilon\}$.
May
27
revised In formal languages, why is $L^0 = \{ \epsilon \}$? Why isn't it the empty set ∅?
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May
27
comment I need some help understanding proofs for an upside-down cycloid being the tautochrone curve. Could someone show me or point me to a simple proof?
There's a straightforward proof in the first chapter of George Simmons' Differential Equations text.
May
26
comment Calculate fractional part of square root without taking square root
Related: Detecting perfect squares faster than by extracting square root
May
21
comment In topology, any relationship on boundary like $Bd(A\cap B)$ and $Bd(A) \cap Bd(B)$?
The conjecture is false even for well-behaved sets. Let $A$ be a disc and $B$ be its complement.
May
21
awarded  Good Answer
May
21
comment If the answer is “no” then “yes” and vice versa type of paradoxes. What are they?
I wrote about the significance of Russell's paradox here: math.stackexchange.com/questions/1086645/…
May
20
comment Lambda calculus typing
Your last question doesn't make sense to me.
May
20
comment Lambda calculus typing
It could be. Depends on who you're talking to. Why is there no $b$ and $e$ for which $b=b\to e$?
May
20
revised Special representation of a number
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May
20
revised Special representation of a number
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May
20
comment Lambda calculus typing
Your conclusion is correct, but the reason isn't quite right. For example, suppose you found $b=p\to (q\to r)$ and also $b=(s\to t)\to u$. Does this fail? No, because you can unify these types by saying that $p=s\to t$ and $u=q\to r$. But in your example, say the type of $y$ is $b$ and the type of $yy$ is $e$. Then you need $b = b\to e$, and there is no such $b$. In this case the unification algorithm fails.
May
20
comment Special representation of a number
Experiments bear out this theory. There are 20 ways to represent 3150 in the form $n=pq+rs$, and this is the most ways for any $n$ under 10,000. But if we start looking at larger primes, there are over ten thousand such $n$ below 200,000; for example there are 20 or more ways to represent each of 170280, 170430, 170436, 170520, 170790, 170940, 170970, 171318, 171780, 171990, 172410…
May
20
revised Special representation of a number
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