Table of Contents
What is a vacuous proof?
Short answer. A vacuous proof is a dangerous thing in formal verification and needs immediate attention. It is an extreme case of a false positive where your checker says that everything is working fine while often checking nothing meaningful.
What is Isinfinity?
Infinity is the idea of something that has no end. In our world we don’t have anything like it. So we imagine traveling on and on, trying hard to get there, but that is not actually infinity. If there is no reason something should stop, then it is infinite.
What is vacuous and trivial proof?
A trivial truth is simply a tautology of logic (sometimes with equality added). This means that a vacuous proof can only be possible in an inconsistent theory (because contradiction entails everything) while a trivial proof is a proof that is valid because formulation of the theorem is a tautology.
What are trivial proofs?
Trivial proofs In some texts, a trivial proof refers to a statement involving a material implication P→Q, where the consequent, Q, is always true. Here, the proof follows immediately by virtue of the definition of material implication, as the implication is true regardless of the truth value of the antecedent P.
How do you prove the Collatz conjecture?
Take any positive integer n . If n is even then divide it by 2 , else do “triple plus one” and get 3n+1 . The conjecture is that for all numbers, this process converges to one….Complete Proof of the Collatz Conjecture.
| Comments: | 8 pages |
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| Cite as: | arXiv:2101.06107 [math.GM] |
| (or arXiv:2101.06107v4 [math.GM] for this version) |
Is there a proof for the Collatz conjecture?
No, the Collatz conjecture has not been proven, hence the term “conjecture.” In fact, Collatz is nowhere near proved. It is among the least tractable problems in all of mathematics. This combined with the problem’s simple statement makes it quite peculiar.