In mathematical logic, a formal calculation is a calculation which is systematic, but without a rigorous justification. This means that we are manipulating the symbols in an expression using a generic substitution, without proving that the necessary conditions hold. Essentially, we are interested in the form of an expression, and not necessarily its underlying meaning. This reasoning can either serve as positive evidence that some statement is true, when it is difficult or unnecessary to provide a proof, or as an inspiration for the creation of new (completely rigorous) definitions.
However, this interpretation of the term formal is not universally accepted, and some consider it to mean quite the opposite: A completely rigorous argument, as in formal mathematical logic.
Other articles related to "formal calculation":
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... sides Now we take a simple antiderivative Because this is a formal calculation, we can also allow ourselves to let and obtain another solution If we have any doubts about our argument, we can always check the ...
Famous quotes containing the words calculation and/or formal:
“To my thinking boomed the Professor, begging the question as usual, the greatest triumph of the human mind was the calculation of Neptune from the observed vagaries of the orbit of Uranus.
And yours, said the P.B.”
—Samuel Beckett (19061989)
“I will not let him stir
Till I have used the approvèd means I have,
With wholesome syrups, drugs, and holy prayers,
To make of him a formal man again.”
—William Shakespeare (15641616)