Another interesting topic that came up in this class was the definition of equal, which (according to out teacher) is "an equivalence relation in which the related objects can be substituted for each other in all meaningful situations." But, as some students pointed out, can you ever prove that two things are equal (since you can't possibly show that they can be substituted for each other in all meaningful situations)? For example, the teacher said that people still argue over whether or not 4/1 = 4. If we really took these definitions into consideration in our other math classes, there would probably be chaos. Just imagine all the work we've done in number theory. Can we really say that some of the things we've proved to be equal are actually equal? What do you guys think?

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