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I was reading book related to Time Complexity, and came up with 4 lines of equations that I could not understand properly, could you please explain why are those true?

1) $n = o(n\log\log n)$

2) $n\log\log n = o(n\log n)$

3) $n\log n = o(n^2)$

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Basically, when you see $f(x)=o(g(x))$, it indicates that $\lim_{x\rightarrow\infty}\frac{f(x)}{g(x)}=0$. If you plug them in, e.g., $\lim_{x\rightarrow\infty}\frac{n}{n\log\log n}=\lim_{x\rightarrow\infty}\frac{1}{\log\log n}=0$, you will see they satisfy it.

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