Den söndag 1 oktober 2017 kl. 21:35:38 UTC+2 skrev John Gabriel: > On Sunday, 1 October 2017 10:21:15 UTC-5, burs...@gmail.com wrote: > > The year 2525, and bird brain John Gabriel schizophrenic > > as usual. First calling Peano crapaxioms, and then in > > another thread presenting induction as a solution. See > > for yourself how schizophrenic you are: > > > > https://groups.google.com/d/msg/sci.math/bgU-4JWvHbY/wAlbdrxPBAAJ > > > > Note: I mentioned only forall, John Gabriel said > > it is induction. But everybody knows that not each > > forall is induction. Should I make an example? For > > example Peano has the following axiom: > > > > forall x (S(x) <> 0) > > > > So you don't need induction to proof: > > > > forall x (S(x) <> 0) > > > > Axiom Nr. 8: > > "For every natural number n, S(n) = 0 is false. That is, > > there is no natural number whose successor is 0." > > https://en.wikipedia.org/wiki/Peano_axioms#Formulation > > > > There are much more examples of universal sentences > > which don't need induction. And there are also universal > > sentences which go beyond Peano, cannot be proved in Peano. > > > > P.S.: There is a slight chance that axiom Nr. 8 is > > redundant, and that it can be proved by induction. I > > dunno, maybe? But this is irrelevant since: > > > > a) Axioms need not be irredundant. > > b) A proof doesn't use induction, if it doesn't use induction, > > so even if an axiom is redundant, if we use it, we did it > > without induction. > > c) Sometimes the situation for axioms is not so simple, > > axioms might be not strictly redundant/irredunant, > > for example it can be that two axioms A1 and A2 are > > slightly overlapping, not allowing to drop either. > > > > Am Sonntag, 1. Oktober 2017 16:26:45 UTC+2 schrieb John Gabriel: > > > Peano was an absolute moron, but if you think that this sounds bad, just wait... most modern math academics have adopted his juvenile "axioms" as part of their math "foundations". I can't imagine anything more ridiculous and what an embarrassment and shame it is to modern academics. > > > > > > Giuseppe Peano was great friends with the tobacco head logician Bertrand Russell the arrogant English nincompoop who wrote a paper close to 200 pages trying to prove that 1+1 = 2. Of course the definition of 2 is 1+1, but this was too simple for primate Russell to understand. These arrogant and incompetent fools left a huge stain on mathematics which has set it back rather than help to improve. > > > > > > The only perfect derivation of numbers is given in my article below. Unfortunately, it took over 2000 years for it to be written. > > > > > > https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel-1 > > > > > > Comments are unwelcome and will be ignored. > > > > > > Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics. > > > > > > email@example.com (MIT) > > > firstname.lastname@example.org (HARVARD) > > > email@example.com (MIT) > > > firstname.lastname@example.org (David Ullrich) > > > email@example.com > > > firstname.lastname@example.org > > Hello my little stupid. > > Peano's Crapaxiom 5 is the induction axiom: > > If a set S of numbers contains zero and also the successor of every number in S, then every number is in S. > > Did you even ever bother to study Peano's crapaxioms? Or did you just memorise them by heart? Stupid boy you are.
One of the axioms being induction does not mean all forall is induction, that doesn't follow.
Most of us have studied it a lot, I have a fondness for number construction. You have never bothered with it. I'd love to see you deal with Eudoxus real numbers and see how you manage to butcher it completely. What are you going to say there? That an almost homomorphism delta function takes on any value?