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An approximation problem
Problem: Let us call an irrational number well approximated by rational numbers if for any natural numbers there exists a rational number such that Solution: 1. Pick Why does it work ? Let’s say we let . Then we have and We now proceed in proving that when is large enough We have So we want …
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On IMO2017 P2
I did IMO 2017 P2 with my friends yesterday. Now I would like to share my thoughts on this problem. Problem: Let be the set of real numbers. Determine all functions such that, for any real numbers and , The initial step must be taking certain values, testing its properties and then start guessing the solution. Well, obviously, the constant function is a solution to the problem. Now…
My name is Ziv. I am a high school Chinese student who love exploring mathematics! Currently, my favorite fields include complex analysis and abstract algebra!
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An approximation problem
Problem: Let us call an irrational number well approximated by rational numbers if for any natural numbers there exists a rational number such that Solution: 1. Pick Why does it work ? Let’s say we let . Then we have and We now proceed in proving that…