If I have an inductive proof of function f, is f(infinity) also true?
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M$2 Answers
So this is not true here...
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M$
Yet again, it depends on the function. It's about which parts form the function, as those parts (or composites) decide the truthfulness of f at infinity. Think only at the special functions like sin, cos, exp, tan, atan, sinh, cosh, ln. A combination of these functions may not subject to a successful proof of what you want.
Add a couple of notches of respect for you... impressive answer
I am not clear on why this is a valid answer. What type of complexity are you referring to?
To establish an inductive proof, I must show that some base case, say f(0) is true, and then show that if f(n) is true, then f(n+1) is true. Linearity need not apply. To give a trivial example, if I want to show that the function f(x) = x^2 is never negative for all x >= 0, I can create such an inductive proof, yet f is not linear.
My question is more of a number theory question, I believe. Certainly an inductive proof is support that f(n) is true for any ordinal number n, but infinite is not actually a number, so I am asking if an inductive proof is valid for establishing the truthfulness of f(infinity) .
