If logic were the sole guide of the teacher

More of continuity, or less of continuity, more derivatives, and so forth. Indeed, from the point of view of logic, these strange functions are the most general; on the other hand those which one meets without searching for them, and which follow simple laws appear as a particular case which does not amount to more than a small corner.In former times when one invented a new function it was for a practical purpose; today one invents them purposely to show up defects in the reasoning of our fathers and one will deduce from them only that.If logic were the sole guide of the teacher, it would be necessary to begin with the most general functions, that is to say with the most bizarre. Its meaning in any particular case resides in the community of mathematicians iphone case, and not necessarily within mathematics itself.

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