Nov 29, 2024 · The principle of mathematical induction does eliminate the possibility of the existence of any finite counterexample. But to say that "it doesn't prove that a statement is …

Sep 27, 2024 · The formalisation at the top of this post shows that mathematical induction proofs are logically valid; thus, if the two premises of an induction proof have been proven true—that …

Feb 9, 2015 · Mathematical induction's validity as a valid proof technique may be established as a consequence of a fundamental axiom concerning the set of positive integers (note: this is only …

Mar 11, 2015 · First, most students do not really understand why mathematical induction is a valid proof technique. That's part of the problem. Second, weak induction and strong induction are …

Now the induction step: If the formula is true for n n, show that it is valid for n + 1 n + 1. In this case (as in many sums) this is just to take the identity for n n and add the next term to both …

Nov 25, 2013 · I am currently taking Discrete Mathematics and while I understand most of the topics covered, the one topic which I still don't quite understand is Mathematical Induction. The …

Nov 26, 2024 · After simplifying this expression, is this the final answer? For every other type of proof we prove that our original statement P(n) P (n) is right ; but mathematical induction …

I dislike the isolation of weak induction. I’d rather see induction taught first in terms of (non-existence) of a least counterexample. Strong induction comes naturally that way, and weak …

Jul 15, 2015 · The base case for a proof that uses mathematical induction may start at any integer whatever. Sometimes you need more than one base case to get a proof started effectively. …

Dec 20, 2025 · For questions about mathematical induction, a method of mathematical proof. Mathematical induction generally proceeds by proving a statement for some integer, called the …