[FOM] inconsistency of P

[Sam Sanders]

An example from my teaching experience:

If one has to teach physics students 'proper' calculus, i.e. with epsilons and deltas, it is helpful to give them intuitive and informal explanations using infinitesimals.  
Usually, they know similar stories that use infinitesimals from other (physics) courses.  
Most of these intuitive stories only really apply to standard functions (in the sense of Nonstandard Analysis), but that is way beyond first or second year students in physics.  
Hence, one 'lie' I gross over is the distinction between standard and nonstandard.

It is a different discussion whether this practice (and NSA in general) is useful for students in mathematics (I believe both are).  

ps: Keith Stroyan once said during a lecture on this very subject: 'We should not lie to our students, but we shouldn't necessarily tell them the entire truth".  
  
> Some of us who don't routinely teach calculus would find it interesting to hear from those who do as to which "lies" are the most helpful in getting students up to speed on the subject.  One could then judge which ones are really necessary for good pedagogy, as opposed to being merely unexamined conventional wisdom about the subject.