Let's build a Production-Grade Bloom Filter in Python

Ever wondered how databases can tell you "this username is definitely not taken" in milliseconds without scanning millions of records? Or how caching systems avoid expensive database lookups for keys that don't exist? The secret is a probabilistic data structure called a Bloom Filter. Let's build one from scratch :- with production features like persistence, serialization, and monitoring. What's a Bloom Filter? A Bloom filter is a space-efficient probabilistic data structure that tells you: "Definitely not in the set" (100% certain) "Probably in the set" (with a configurable false positive rate) It's like a bouncer who sometimes lets the wrong person in but never turns away someone who should be there. The Trade-off Aspect Traditional Set Bloom Filter Space O(n) per element ~2-10 bytes per element Time O(1) average O(k) where k ~ 5-10 False Positives None Configurable (0.1% - 5%) Deletions Supported Not supported For 10 million items, a hash set might use 500MB+ of memory. A Bloom filt