Tagged Questions
9
votes
5answers
401 views
Why König's lemma isn't “obvious”?
I keep facing König's lemma "Every finitely branching infinite tree over $\mathbb{N}$ has infinite branch". Why it is not taken "obvious" but needs a careful proof?
It seems somewhat obvious, but I ...
0
votes
1answer
63 views
Ramsey's theorem.
For $k=2$, from this post A "geometrical" representation for Ramsey's theorem, how one can deduce the theorem from Constant $f:[\mathbb{N}]^2\to \{1,2\}$ (part 2), or by knowing that ...
10
votes
1answer
84 views
Coloring of positive integers
Suppose $f:\mathbb{Z}^+\longrightarrow X$ is a function, with $X$ a finite set. Is it true that there are $a,b\in\mathbb{Z}^+$ such that $f(a)=f(b)=f(a+b)$.
