freshman’s dream error
The name “freshman’s dream theorem” comes from the fact that people who are unfamiliar with mathematics commonly make the error of distributing exponents over addition
and/or subtraction, typically when working in fields of characteristic zero. An example is the equation for . The equation is incorrect unless or . By no means does the exponent need to be a natural number
or an integer for this error to occur. An example of this is the equation for with and . This equation can be rewritten using the exponent , and again, the equation is incorrect unless or .
An easy way to explain to someone who is under the impression that exponents distribute over addition and/or subtraction is to provide a counterexample. For instance, when and , we have:
On the other hand, the freshman’s dream theorem yields some instances in which exponents can be distributed over addition and/or subtraction.