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answered Fun math books for 8 year old with math aptitude
14m
answered Is $\langle\mathbb Q^+, *\rangle$ a monoid?
8h
comment Indicator Function Distributive Property Proof
@Sunhwa: My pleasure. (I’d normally give a hint rather than a complete answer, but when you’re just starting, a fully worked out example can be very helpful.)
8h
answered Indicator Function Distributive Property Proof
9h
comment Indicator Function Distributive Property Proof
You’re welcome!
9h
comment Indicator Function Distributive Property Proof
You are correct; the book’s expression is the indicator function corresponding to $\Bbb A\land(\Bbb B\lor\Bbb C)$, not to $\Bbb A\lor(\Bbb B\land\Bbb C)$.
10h
answered Conting Homomorphisms from a cyle to another graph
11h
comment Given 5 integers show that you can find two whose sum or difference is divisible by 6.
... resize to fit what’s inside: \left\lceil\frac65\right\rceil gives $\left\lceil\frac65\right\rceil$.)
11h
comment Given 5 integers show that you can find two whose sum or difference is divisible by 6.
This won’t work, I’m afraid: a function from $A$ to $B$ assigns a member of $B$ to each of the possible remainders. What you’ve shown is that if you do that, two remainders will be assigned the same member of $B$; what you need is exactly the opposite, two members of $B$ with the same remainder. Unfortunately, you can’t necessarily get that: $B$ could be $\{1,2,3,4,5\}$, for instance. In that case, however, it turns out that you can always find two members of $B$ whose remainders sum to $6$. (By the way, if you use \left\lceil and \right\rceil, the ceiling brackets will automatically ...
11h
comment An example of open closed continuous image of $T_2$-space that is not $T_2$
@Zed: You’re right about $W$, and the $U_i$ should have been $U$; I changed the writeup at one point and evidently missed a few spots. The last paragraph was a case of my mind getting ahead of my fingers. Thanks for catching these; they should be fixed now.
11h
revised An example of open closed continuous image of $T_2$-space that is not $T_2$
Typos. Fixed last paragraph, where my mind ran ahead of my fingers originally.
11h
revised An example of open closed continuous image of $T_2$-space that is not $T_2$
Typos.
12h
awarded  Nice Answer
19h
comment Number of injective maps from one finite set to another
Yes, it is, as is the reasoning.
23h
comment Unclear about the definition of “closed”?
@Kalpesh: Right – and that’s exactly the point: $0$ is not contained in that set, but it is a limit point of that set, because every nbhd of $0$ contains points of $(0,1]$.
1d
answered Graph Theory: A graph is acyclic then parent label is smaller than children label
1d
revised partitions and generating functions ( combinatorics )
added 359 characters in body
1d
comment partitions and generating functions ( combinatorics )
This is perfectly clear, but I’ll edit it to make it even more obvious.
1d
answered If $X$ is a polish space, how do we find an equivalent metric under wich $X$ is a totally bounded?
1d
comment $f$ is continuous, $f : X \to X$, $X$ compact, and $f$ has an $\epsilon$-fixed point for each $\epsilon > 0$. Show $f$ has a fixed point.
Every compact metric space is sequentially compact.