Database normalization is a method for structuring your database schema in a way that helps:
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"Data integrity" refers to the accuracy and consistency of data. For example, if a user's age is stored in a database, rather than their birthday, that data becomes incorrect automatically with the passage of time.
It would be better to store a birthday and calculate the age as needed.
"Data redundancy" occurs when the same piece of data is stored in multiple places. For example: saving the same file multiple times to different hard drives.
Data redundancy can be problematic, especially when data in one place is changed such that the data is no longer consistent across all copies of that data.