### re: What is O(log n)? Learn Big O Logarithmic Time Complexity VIEW POST

re: Big theta and big Omega are upper bounds and lower bounds, right? But in software engineering, we don't mind the upper or lower bounds that's why w...

Not quite. Big O is the upper-bound (longest possible run time), while big-Ω is the lower bound (shortest possible run time). It's big-Θ that's the combination of the two, although it can only be used if the upper and lower bounds are the same.

While big-O is the most commonly useful, since we most often care about the longest possible running time of a particular scenario (e.g. of worst-case), it still has a precise meaning.

When we say "the function is at least O(n)", we're almost always misappropriating big-O (upper bound) to describe big-Ω (lower bound).

What's further, when we say "the function always has a runtime of O(n²)", we're really meaning "Θ(n²)"; it's not just the upper bound, but both bounds at once.

To put that another way, "lower bound" means "a runtime of at least", and "upper bound" means "a runtime no greater than". This has nothing to do with best-case/worst-case, as we are always speaking about the runtime of worst-case, unless explicitly stated otherwise.

Take a look at my comment on that article I linked to for more details.

// , If it gets really big, it's big-Θ-Lawd: youtube.com/watch?v=zlplCs00wTE

"Your time complexity is so bad, not even the TARDIS can handle it."

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