Big-O Notation for Sequences Coincides with General Definition
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Let $\N$ be given the discrete topology.
The following are equivalent:
- $(1): \quad$ $a_n = O(b_n)$, where $O$ denotes big-O notation for sequences
- $(2): \quad$ $a_n = O(b_n)$, where $O$ stands for the general definition of big-O notation