Build a Bloom Filter and Watch ‘Probably Present’ Become a False Positive

A Bloom filter can say an item is definitely absent or probably present. It cannot prove membership. The easiest way to learn that distinction is to generate a false positive yourself.

import hashlib

class Bloom:

    def __init__(self, bits=128, hashes=3):

        self.bits=[0]*bits; self.k=hashes

    def positions(self, value):

        raw=value.encode()

        for i in range(self.k):

            yield int.from_bytes(hashlib.sha256(bytes([i])+raw).digest()[:8])%len(self.bits)

    def add(self, value):

        for p in self.positions(value): self.bits[p]=1

    def maybe(self, value):

        return all(self.bits[p] for p in self.positions(value))

Insert deterministic values item-0000 through item-0099. Then query new values until maybe() returns true. Print the first false positive with bit count, hash count, inserted count, and query count.

Experiment table

Use the same input sequence for each row. Test empty filters, repeated insertion, known members, and a deliberately undersized filter. Expected invariant: inserted items have no false negatives; absent items may be false positives.

Do not replace an authorization check or billing record with a Bloom filter. Use it as a cheap prefilter followed by an authoritative lookup when maybe() is true.

Python's hash choices here are educational, not a production recommendation, and the measured rate is not universal. Which workload can tolerate an extra lookup but never a false negative?