I made these assertions against the 'out of box' use case. Meaning the use of MySQL and Redis as they come against each other without indexing.
I also believe with indexing the best relational databases can achieve is O{log n}. More of this here (databases O-notation).
While Redis is an in-memory store typically meaning your Redis store sits on the RAM of your server, therefore allowing it access to data structures adapted to memory storage. Hence why Redis can achieve O-notations such as O{1 + n/k). More of this here (How Redis claims O(1) lookup).
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I made these assertions against the 'out of box' use case. Meaning the use of MySQL and Redis as they come against each other without indexing.
I also believe with indexing the best relational databases can achieve is O{log n}. More of this here (databases O-notation).
While Redis is an in-memory store typically meaning your Redis store sits on the RAM of your server, therefore allowing it access to data structures adapted to memory storage. Hence why Redis can achieve O-notations such as O{1 + n/k). More of this here (How Redis claims O(1) lookup).