discrete mathematics - Proof by induction that $1^2 + 3^2 + 5^2 ...
2016年3月30日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Why is mathematical induction a valid proof technique?
2015年2月9日 · 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 …
What exactly is the difference between weak and strong induction?
2015年3月11日 · 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 …
What's the difference between simple induction and strong …
It is not why we still have "weak" induction - it's why we still have "strong" induction when this is not actually any stronger. My opinion is that the reason this distinction remains is that it serves …
Mathematical Induction (summation): $\sum^n_{k=1} k2^k =(n …
I am stuck on this question from the IB Cambridge HL math text book about Mathematical induction. I am sorry about the bad formatting I am new and have no idea how to write the …
number theory - Proof by induction with two variables
Regular induction requires a base case and an inductive step. When we increase to two variables, we still require a base case but now need two inductive steps. We'll prove the statement for …
Mathematical Induction Proofs - Mathematics Stack Exchange
2019年12月13日 · I've really been struggling with mathematical induction. I've been trying to follow my book the best I can. I feel like my proofs are correct. But then again I have my …
logic - Structural Induction vs Normal (Mathematical) Induction ...
As I understand it now, Noetherian induction (a.k.a. well-founded induction?) is the most general of the concepts, mathematical induction is Noetherian induction restricted to natural numbers, …
Induction on Real Numbers - Mathematics Stack Exchange
You can interpret mathematical induction on the natural numbers simply as "proof according to the method using which the world in question was constructed". The construction of …
discrete mathematics - Formal logical form of mathematical …
2024年9月27日 · 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 …