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2d
comment How do mathematicians find the underlying idea?
Experience as much mathematics as you can. Some techniques will appear over and over (such as adding and subtracting the same value) and start to become a part of your repertoire naturally.
2d
comment Show that the collection of all open subsets of $X$ that are contained in $Y$ is a topology on $Y$.
By the way, this is known as the subspace topology induced by $Y$.
2d
comment Show that the collection of all open subsets of $X$ that are contained in $Y$ is a topology on $Y$.
"If all open subsets of $X$ that are contained in $Y$ is not a topology on $Y$, then there is some open subset of $Y$ that is not contained in $X$." I don't believe this follows. Perhaps the subsets fail to be a topology for some other reason, such as not satisfying the requirement for unions or intersections.
2d
comment Stating the induction hypothesis
I would go with (3) except, as Andre suggests, you should not overload the meaning of $n$. It is a free variable in the statement of your proposition, and you use it again to refer to a specific value where you assume the inequality holds. It would be better to replace $n$ with $k$.
Aug
27
comment Chart of Rounds for a Game
This may be relevant: en.wikipedia.org/wiki/Block_design
Aug
25
revised Number of Ways to Draw a Pair in a Poker Deck
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Aug
25
revised Number of Ways to Draw a Pair in a Poker Deck
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Aug
25
answered Number of Ways to Draw a Pair in a Poker Deck
Aug
25
comment Number of Ways to Draw a Pair in a Poker Deck
The original question does not ask for probability.
Aug
25
revised Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
added 1 character in body; edited tags; edited title
Aug
25
answered Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
Aug
24
revised Weighting In a Function
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Aug
24
revised Weighting In a Function
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Aug
24
answered Weighting In a Function
Aug
20
awarded  Good Answer
Aug
14
revised How do I approach on proving the following fact - 1. Every path is Bipartite?
added 2 characters in body
Aug
14
comment Zeno's Track Time
"the series 1/(2^n), which goes to 0 as n goes to infinity, therefore converging on 0." The sequence of terms $\frac{1}{2^n}$ converges to 0, but the series $\sum_{n = 1}^\infty \frac{1}{2^n}$ converges to 1. Moreover, a sequence of terms may converge to 0 and yet the series can be divergent. The series $\sum_{n = 1}^\infty \frac{1}{n}$ is an example.
Aug
13
comment Bases having countable subfamilies which are bases in second countable space
@Akaichan $\Gamma$ is some arbitrary indexing set.
Aug
1
comment Why is every point in an open interval $(a,b)$ not a limit point?
I'm voting to close this question as off-topic because OP retracted question.
Aug
1
comment Graph Theory: How quickly will triadic closure create a complete graph?
@DrXorile I took the operation to mean that a single step involved the identification of all such $\{i, j, k\}$ triples in the graph and the addition all the resulting $ik$ edges simultaneously. For example, the star becomes a complete graph in one step, since any two vertices are connected by a path of length at most two.