Equations are not only ubiquitous in mathematics, they are also heavily used in programming. We have used equations to state what a function should do with examples, we have used them to evaluate expressions by hand, and we have added them as test cases to the Definitions window. For example, if our goal is to define Fahrenheit-+ Celsius, we might have added our examples as test cases as follows:
After clicking the Execute button we can compare the two numbers. If they are equal, we know our function works.
As our results become more and more complex, comparing values becomes more and more tedious. Using =, we can instead translate these equations into claims:
Now, if all claims evaluate to true, we know that our function works for the specified examples. If we see a false anywhere, something is still wrong.
Reformulate the test cases for exercises 2.2.1, 2.2.2, 2.2.3, and 2.2.4 as claims.
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