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 Yearling
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Sep
1
comment Showing that a set is a basis of a field as a vector space over a subset of that field
It means that the defintion of basis of vector space applies. Btw, it is not needed that $F$ is a field; vector space over $L$ is enough.
Sep
1
comment Example of a function which is non-lipschitz but satisfies some weaker notion of linear growth
Maybe $f(x)=-1_{\mathbb Q}(x)$ ?
Sep
1
comment How to calculate the cardinality of the intersection of three sets?
This makes $n(A)=n(A\cap \bar B \cap \bar C) + n(A\cap \bar B \cap C)+n(A\cap B \cap \bar C)+n(A\cap B \cap C) = (27+k)+(25-k)+(16-k)+k = 68$ as required.
Sep
1
answered Fixed point property in topology
Sep
1
comment How many solutions are there for the congruence $x^{14}+x^7+1 \equiv 0 \; (\text{mod } 343)$?
Multiply with $x^7-1$.
Sep
1
comment Is an Invariant set Connected?
$\mathbb R^n$ itself is a connected invariant set, and maximal with these properties. At the other end of the spectrum, the trajectory of a single starting point is also a connected invariant set
Sep
1
comment Solve $yx^2-zx+v=0$ for x?
@Kenshin But whatever you do, you won't get a different result. (Except that you should be careful if $y$ might me zero)
Sep
1
comment Fixed point property in topology
a) consider $X\times \mathbb R$ and $(x,r)\mapsto (x,r+1)$.
Sep
1
awarded  Yearling
Aug
31
comment Variation of Monty Hall problem
Yes, and I am answering that. Before the accident, there was a $\frac13$ chance of picking (or having pocked) the right door. If the accident had revealed the car, switching or not switching would both give you a goat, by the way
Aug
31
answered Variation of Monty Hall problem
Aug
31
comment Folding sheets of paper
There are many lengths. What kind of description do you expect?
Aug
31
comment How I can imply that the supremum is in a set S?
Yes, that is one way to proceed.
Aug
31
comment How to calculate the cardinality of the intersection of three sets?
Yes, starting only from the original info, we can only input $n(A\cup B\cup C)\le 151$ into the i/e principle, which gives $n(A\cap B\cap C)\le 30$.
Aug
31
revised How to calculate the cardinality of the intersection of three sets?
added 99 characters in body
Aug
31
answered How to calculate the cardinality of the intersection of three sets?
Aug
31
comment Prove tautology without truth table
... and maybe associativity (used here implicitly by not using parentheses) needs to be mentioned explicitly.
Aug
31
comment Why induction cannot be used for infinite sets?
Not to mention that the more general statement $\left(\bigcup_{i\in I} A_i\right)^c = \bigcap_{i\in I} A_i^c$ holds - with an arbitrary index set $I$.
Aug
28
answered The probability of $n$ being a square, given the units-digit in its decimal representation
Aug
28
comment how to fairly select a leader
Why not allow people the freedom to vote about unkown candidates? Such as: Of the interviews with $a,b,c$, the last two turned out so awful, it is safe to assume that $d$ is better than $b,c$, so my priority is $adbc$ (or perhaps mixed with $dabc$).