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I don't grasp how to the activities are tied together.

marked as duplicate by Murch, Salvador Dali, D.H. - bitcoin.se Jan 4 '14 at 20:57

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miners are like accountants that do accounting for a business. they run the software that does the maths to "verify" transactions are valid. these accountants (miners) are rewarded for their time / effort in creating new ledger pages (blocks in the blockchain), which they in turn need to verify transactions

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