Relational Algebra in databases

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Chromium
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so in my intro to databases class, so far we have only learned about the various relational algebra operators. So far, relational algebra just seems like this purely theoretical concept that has no practical purpose. So, I was wondering: is relational algebra used commercially as a query language? Is it utilized at all in industry?

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SQL is based on relational algebra. Have you written any queries yet? When you do, you'll do things like selection, projection, joins, unions, etc all the time. (I assume that's the sort of operations you're learning about, anyway.)
 
No, I haven't written any queries yet. But if SQL is based on relational algebra, does that mean that most, if not all, relational database management systems have relational algebra operations somewhere in their implementation? For example, if I call a SELECT operation on a table, am I really calling a SELECT function that has the relational algebra project operation somewhere in its definition?