Timeline for Good, simple examples of induction?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 4, 2021 at 3:58 | comment | added | user2252440 | Interestingly enough --- the proof is essentially the same proof as used for the division algorithm. Given $k$, we know that $k-2$ is either even or odd by induction, and in each case we can increment by $2$ to show that $k$ is either even or odd. The division algorithm uses the exact same proof, with $2$ replaced by an arbitrary denominator. | |
| Nov 5, 2021 at 20:51 | comment | added | Steven Gubkin | I actually like this one. Generally the definitions are "x is even if x=2k for some integer k", and "x is odd if x=2k+1 for some integer k". Given these definitions, it does require proof that any number is either even or odd. All such proofs will require induction. | |
| Jan 8, 2019 at 23:27 | comment | added | user507 | It's hard to evaluate the appropriateness of this without understanding what definitions and axioms are assumed. If odd numbers are defined as those that aren't even, then this is trivial. Would this be proved from the Peano axioms...? | |
| Apr 22, 2014 at 17:40 | comment | added | Brendan W. Sullivan | Could you expand on this and explain how a student would prove this by induction? As written so succinctly, this is much better suited as a comment. | |
| S Apr 22, 2014 at 17:06 | review | Low quality posts | |||
| Apr 23, 2014 at 9:14 | |||||
| S Apr 22, 2014 at 17:06 | review | First posts | |||
| Apr 22, 2014 at 17:40 | |||||
| Apr 22, 2014 at 16:47 | history | answered | Colin Tan | CC BY-SA 3.0 |