5 ms·
The proof in the tweet gives steps to getting a solution, and the solution works. In what way is that not showing that the solution exists?
by johnday 5y ago
The proof in the tweet gives steps to getting a solution, and the solution works. In what way is that not showing that the solution exists?
- Jeff_Brown 5y agoThe tweet only shows what J is, conditional on that there is a solution.
- quchen 5y agoIsn't that exactly how any constructive proof works?
- Jeff_Brown 5y agoI suppose it depends on your definitions, but most constructive proofs construct an entire solution -- that is, leaving no variables free unless the solution applies to any value of them. This only solves for J assuming the others can be solved for.
- yodsanklai 5y agoA constructive proof would exhibit a solution. In that case, it has been shown that if a solution exists, it must be that J=6. With this additional information, you can try and find the other digit and conclude the proof (or in the case there's no solution, reach a contradiction). I don't know how this type of proof is called in English but it's quite common. First come up with necessary conditions on your potential solution, and then you use these conditions to build an actual solution.
- DinnerAtEight 5y agoConsider the following problem: ABC DEF + GHI ---------- 12300000J where each letter represents a unique digit. The logic in the tweet would give the same value for J as the original problem, but in this case there is no solution.