Does it store all the letters one writes? (8)

I believe the answer is:

alphabet

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'letters one writes?' is the definition.
I know that 'letters' relates to this answer.

I can't explain the remainder of the clue.

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(Other definitions for alphabet that I've seen before include "Complete set of letters" , "Pale bath (anag.)" , "Confusing assortment of initials" , "Fundamental language components" , "Letters, symbols used in a writing system" .)

I've seen this clue in The Times and The Sun.

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