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Okay, so now we're going to answer the question. So if we want
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to consider all these inputs, and run them all on the software,
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let's see how it will work. Let's assume that these are, 32
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bit integers. So at this point what we will have is, a
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number of combination, which is 2 to the 32, times 2 to
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the 32. They're two integers. This is equal to 2 to the
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64, which in turn, is more or less equal, to 10 to
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the 19. So 10 to the 19 is the number of tests that
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we need to run to cover the whole domain. Now let's assume
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that we can run one test per nanosecond. So what that means
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is that we can run 10 to the 9 tests per second,
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and that's a lot. If we do the math, that results in 10
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to the 10 seconds over all, because we have 10 to the
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19 tests, we could run 10 to the 9 tests per second
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so, we do the math, and we can run all these tests
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in 10 to the 10 seconds. And what that corresponds to, it's about
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600 years, so a lot of time. So even for such
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a simple problem, a problem that takes two integers and adds them,
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it will take more than 500 years to test it exhaustively. So
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the bottom line here is that we just can't do exhaustive testing.
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