TASK DEFINITION: In this task, you need to translate the given English sentence to Polish language.
PROBLEM: and so to out-compete those who couldn't, 

SOLUTION: a tych, którzy tego nie potrafili, wykluczyć. 

PROBLEM: If x is an arbitrary member of Rn, Let me write like this. 

SOLUTION: Jeżeli x jest dowolnym elementem Rn -- zapiszę to tak. 

PROBLEM: And actually when we are closest to the sun, so Earth is right over here, there's a word for that, 

SOLUTION:
I kiedy jesteśmy najbliżej słońca, więc Ziemia jest tutaj, jest na to słowo,