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I was reading “Introduction to Algorithms” by CLRS and it says

Note that f(n) = Θ(g(n)) implies f(n) = O(g(n)) since Θ notation is a stronger notation than O notation. Written set theoretically, we have Θ(g(n)) ⊆ O (g(n)) .

This means that Θ is a subset of O . Both the statements seem contradictory.

Please help.

Thanks!

I was reading “Introduction to Algorithms” by CLRS and it says

Note that f(n) = Θ(g(n)) implies f(n) = O(g(n)) since Θ notation is a stronger notation than O notation. Written set theoretically, we have Θ(g(n)) ⊆ O (g(n)) .

This means that Θ is a subset of O . Both the statements seem contradictory.