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Correction: Induction is how we can understand that a property holds for all finite values. It seems that you object to the commonly accepted meaning of "..."
by recursive 10y ago
Correction: Induction is how we can understand that a property holds for all finite values.
It seems that you object to the commonly accepted meaning of "...".
- kazinator 10y agoSo you're saying that "for all positive integers n : property(n)" means that property(k) might not hold for some k that is not a "finite value"? The only problem is that this not-finite value does not occur among the integers; thus the inductive procession doesn't actually have that value k as its target. It does not lie in its path, so to speak. > It seems that you object to the commonly accepted meaning of "...". I formulated it as a limit and stated that it denotes 1 in the case of 0.999... How do I object?