Jibberish-example.txt S2013
This example solves
x + y + z = 1,
y + 3z = 4,
z = 5.
Back-Substitution by the jibberish method
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x + y + z = 1,
y + 3z = 4,
z = 5.
y=4-3(5)=-11
x=1-5-(-11)=7
What's wrong with it? (1) No answer; (2) No readable details. And if
there was a mistake, who could find it?
Back-Substitution by frame sequences
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x + y + z = 1,
y + 3z = 4,
z = 5.
x + y + z = 1,
y = -11, combo(3,2,-3)
z = 5.
x + y = -4, combo(3,1,-1)
y = -11,
z = 5.
x = 7, combo(2,1,-1)
y = -11,
z = 5.
The answer is x=7, y=-11, z=5, steps documented above.
Arguments for and against
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1. Jibberish is faster.
2. Jibberish can silently get the wrong answer.
3. Jibberish fails miserably when there are free variables.
It is problematic to check a free variable answer.
4. Frame sequences take too long to write.
5. Frame sequences get the right answer even if there are free variables.