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Idempotent is an adjective to describe a process that gives you the same result no matter how many times you run it.

For a mathematical example, adding 1 changes the results, but multiplying by 1 is idempotent. When you add 1 to a number and then add 1 again, you get different results. If you multiply a number by 1 and multiply by 1 again, you do get the same result.

A more real-world example of idempotency is the process of saving a file in a word processor. Given the same inputs (i.e. the same document contents), clicking "Save" one time will leave your system in the exact same state as clicking "Save" five times in a row.

A non-idempotent version of the "Save" button might do something like "Append the paragraph I just wrote to the end of the file". Doing that five times in a row will not leave you in the same state as doing it one time; your most recent paragraph would have duplicates.

If word processors only gave us non-idempotent "Append paragraph" / "Update paragraph" / "Delete paragraph" operations, then saving our document changes would be a lot more difficult! We'd have to keep track of which paragraphs we previously saved, and either make sure to not save them again or have a process in place to regularly clean up duplicate paragraphs. The implementation of the "Save" button in word processors takes the collection of low-level non-idempotent filesystem operations (read/append/overwrite/delete), and systematically runs them in a certain order so that the user doesn't have to deal with the non-idempotency. The user can just focus on writing -- choosing words, editing for clarity, ensuring paragraphs aren't too long, etc. -- and the word processor deals with making sure the words get persisted properly to disk.

This word processing analogy is very similar to what dbt does for data transformation: it takes the collection of low-level non-idempotent database operations (SELECT/INSERT/UPDATE/DELETE -- collectively known as DML statements), and systematically runs them in a certain order so that analytics engineers don't have to deal with non-idempotency. We can just focus on the data -- choosing good model and column names, documenting them, ensuring data consumers can understand them, etc. -- and dbt run will make sure the database ends up in the right state.