Big O, Theta, and big Omega notation

Based on my understanding, big O is essentially similar to theta notation but can include anything bigger than the given function (eg n^3 = O(n^4), n^3 = O(n^5) , etc.), and big Omega includes anything smaller than the given function ( n^3 = Ω(n^2 ), etc.).

However, my professor said the other day that n^0.79 = Ω(n^0.8) , while he was doing an exercise that involved the master theorem.

Why/how is this true when n^0.8 is larger than n^0.79 ?

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You have big O and big Omega backwards. Big O is everything the "same" or smaller than the function.

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