On 14 April 2017 at 17:59, Bruno Marchal <[email protected]> wrote:
> On 13 Apr 2017, at 19:26, David Nyman wrote: > > On 12 April 2017 at 20:59, Bruno Marchal <[email protected]> wrote: > > 2 ^(2^9) * (3^2) * (5^17) * (7^2) * (11^21) *(13^2) * (17*17) * 3 ^ >> <exercise! :) > > > > Oh, I see what you mean: > > 3 ^(2^17) * (3^0) * (5^21) * (7^0) * (11^17) > > > > Now, you see it was easy, and, like me, you go faaaar ... too much > quickly. > > Even without quoting the dictionary we can suspect some mistake. And I > hope I will not put my finger where it might hurt in case you have been > mentally abused by a sadistic mathematical teacher! > Possibly, but I think I've recovered from any lingering PMSD ;) > That one would ask you what is the value of (3^0) ? and what is the value > of (7^0)? > > And you would panic, thinking like ... hmm... er... 3^2 = 3 * 3, 3^1 = 3, > 3^0 = ...... !!! ..... gosh that one is tricky! > Fortunately you had explained well that it was just a coding system. In fact in the past I have managed to disabuse myself of unnecessary confusions of this sort by realising that something was simply a notation or naming convention. Are irrational numbers, after all, insane? And why is x^0 always 1? (that way you can always add the exponents). > Well, (a^b) * (a ^ c) = a ^(b + c), that is obvious for a, b, c natural > numbers, and if you want keep this true for all integers, you will have > that 3^0 = 3^(5 - 5) = 3^(5 +(-5)) = (3^5) *(3^(-5)) = (again to keep that > law on the integers) = (3^5)/(3^5) = 1. > > same reasoning for (7^0) = 1. > > But 1 is not a prime number, and if we allow it in our coding, it would > become ambiguous. In fact 1 has been thrown out of the prime to get a > simple enunciation of the fundamental theorem of arithmetic: there is only > one decomposition into prime factors. if 1 was a prime number, you can add > it, as a factor where you want! > > That is why, normally, 0 has been represented by non null number, as any > number ^ 0 = 1. > > I say normally, I will now search the dictionary logic-arithmetic (seen as > languages), and I pray I did not make a typo! > > I said: > > So let us denote the logical and arithmetical symbols v, &, ->, ~, E, A, > t, f, "(", ")" =, 0, s, +, * > by the first odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, > 27, 29, > > > So, I did not (at least here). 0 has been represented by 23. (If my > glasses does not fail me). Let us verify * is 29, + is 27, s is 25, 0 is 23. > (A chance my recent cataract surgery has succeed! I have an implant!). > I see (and so do you, I trust). Good health! > > So you should have written: > > 3 ^(2^17) * (3^23) * (5^21) * (7^23) * (11^17) > > > (I guess my talk about was not necessary, .. you did just forget to > represent 0, with a notion known by the machine. > > Yes, I suspected I was succumbing to the use/mention distinction, which you warned me about . B ut alas I looked too quick ly and managed to miss wh ere the symbol for 0 had been mentioned , s o I relied on the expectation that you would kindly correct me. Thanks! > > > PS Are "(" and ")" meant to be the same? > > > Ah! Now, that is *my* error, which you should not have copied, given that > you detect it. ts, ts, ts .... > So we were equally sloppy in this case! Mea culpa though. > > So the correct answer is > > 3 ^(2^17) * (3^23) * (5^21) * (7^23) * (11^19) > > > And so the proof > > Ax(x=x) > (0 = 0) > > is translated in arithmetic-language in the number > > > 2 ^[(2^9) * (3^2) * (5^17) * (7^2) * (11^21) *(13^2) * (17*17)] * 3 ^ > [(2^17) >> * (3^23) * (5^21) * (7^23) * (11^19)] > > > > The only important things is to see that this is just one number, written > s(s(s(s(s(s(s(s ... s(0)))))...), and quite huge (!). Once the machine > believes in addition and multiplication, it will denote the proof, and the > machine will be able to answer question like "does a variable occur in that > proof?", etc. > > Very good David, welcome to logic! (and sorry for being long, and probably > too short in my next answer to the other posts as ... time flies like an > arrow). > And fruit flies like a banana! David > > Bruno > > > > > David > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
