Yes, but induction is problematic in the real world because a great many real world problems do not trivially reduce to an algebraic function or similar that people will readily accept as axiomatic. It works in mathematics because there is generally universal acceptance of the axioms and their derivatives. In the real world the selection of the axioms themselves are major points of contention.
This is the reason most useful reasoning mechanisms in the real world don't really require the implicit assertion of additional axioms and definitions beyond the underlying mathematics e.g. first order logic and Bayes theorem. It is hard do induction when the assertion being proved is not grounded in rock-solid axioms.
It's not hard to do--it's all to easy to do. It's just really, really hard on us, from time to time, when we entirely trust the results.
Focusing on reality works, nothing else makes sense.