Correctness means the produce does what it was intended to do
A formal problem statement is called a formal specification
Usually programmers use testing based on passing tests or test cases but the number of test cases are finite
Mathematics can be used to prove a program does what it is supposed to do
Correct by Construction, before you write the program you focus on making sure it's correct rather than writing the program and testing it aggressively to discover it is correct by passing test cases
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I really appreciate your writing more than just posting videos. Information can be consumed so much quicker, and with so much more flexibility, by reading than by watching a video. Your writing especially is very good stuff to read!