On Sunday, 2 March 2014 02:41:00 UTC+2, Wizard-Of-Oz wrote: > John Gabriel <firstname.lastname@example.org> wrote in > > news:email@example.com: > > > > > This comment is intended as a service to those students who will > > > stumble on pile of trash called sci.math. > > > > > > I discuss the so-called Peano "axioms". But before I do, I must define > > > what the words axiom and postulate mean because most idiots are unable > > > to differentiate between the two. > > > > > > Postulate: an *assertion* assumed to be true, as a basis of inference. > > > Axiom: a self-evident fact, known to be true, and used as a basis of > > > inference. > > > > > > > > > The five Peano "axioms" are stated as follows: > > > > > > 1. Zero is a natural number. > > > > > > I was a teenager when I first read that. My first response was a good > > > chuckle. How could this useless information be written in an > > > Encyclopedia with the reputation of Britannica? > > > > > > Our bonobo mathematician Peano introduces two terms, the subject > > > (zero) and a qualified object (natural number). You are supposed to > > > know what these are, except the only problem, is that the imbeciles > > > (professors of math and mathematicians) don't know what is a > > > magnitude, never mind a number. As for a natural number, our Simian > > > friends in universities worldwide, have no idea how much thought and > > > effort went into the construction of the natural numbers, that was > > > made possible by ratios of equal magnitudes. > > > > > > So, the first so-called "axiom" contains two undefined and unqualified > > > terms. You shall see how rigorous and sound John Gabriel's axioms are > > > at the end of this comment. > > > > > > Without any proof and no justification Peano 1 tells us that zero is a > > > *number*, but not just any rational number, it is a *natural number*. > > > That you don't know what is a natural number, is your problem. > > > > > > You can ask: What is zero? What is a number? What is a "natural > > > number"? And the idiot Peano simply stares at you blankly. > > > > > > 2. Every natural number has a successor in the natural numbers. > > > > > > Peano 2 gets more interesting. After introducing the natural number, > > > the next bombshell is that there is *more than one natural number*! > > > :-) But if this were not shocking enough, we see that these numbers > > > have successors (whatever the fuck that means). So, since we are not > > > told what a successor means, we simply assume that there exists some > > > kind of order such that one number follows the number before it. > > > Spaghetti brain Peano seemed to think these were sound concepts. His > > > fellow primate Bertrand Russell once said that Peano had a sharpness > > > of mind. From this, can we infer the Russell make have lost a > > > substantial amount of brain cells to tobacco smoking? Hmmm. > > > > > > > > > 3. Zero is not the successor of any natural number. > > > > > > Peano 3 tells us that the in the imagined ordering, zero appears > > > first. Never mind that a standard set does not care about the order of > > > elements. Does this mean that if each set is like a brown bag, then if > > > I look inside, the first object I shall see is zero? :-) All natural > > > numbers can be written as S(x), but not 0 according to the imbecile > > > Peano. That's what Peano 3 is saying. > > > > > > 4. If the successor of two natural numbers is the same, then the two > > > original numbers are the same. > > > > > > Peano 4 tells us S(x)=S(y) => x=y. What a profound statement! :-) > > > This introduces the vague notion of difference. > > > > > > 5. If a set contains zero and the successor of every number is in the > > > set, then the set contains the natural numbers. > > > > > > There are so many assumptions in Peano 5, that it's hard to even think > > > of where to begin addressing the bullshit. > > > > > > It infuriates me that the amoebas on this forum DARED to compare my > > > axioms with this fucking rot. > > > > > > To subscribe to such rot exposes your lack of intelligence. > > > > > > And now, for the sound construction of numbers from scratch and the > > > new axioms: > > > > > > Construction of rational numbers: > > > > > > > > > 1. A magnitude is the idea of size of extent. We can either tell that > > > two magnitudes are equal or not. If we can tell they are not equal, > > > then we know which is smaller or bigger, but we can't tell how much > > > bigger or smaller. This is called qualitative measurement (without > > > numbers). > > > > > > 2. We can form ratios of magnitudes. AB : CD where AB and CD are line > > > segments. The expression AB : CD means the comparison of magnitudes AB > > > and CD. > > > > > > 3. A ratio of equal magnitudes, say AB : AB or CD : CD allows us to > > > use either as the standard of measurement, that is, the unit. The unit > > > is a ratio of equal magnitudes. > > > > > > 4. The unit enables us now to compare AB and CD if both are exact > > > multiples of the unit that measures both. We can now perform > > > quantitative measurement, because we can tell how much greater AB is > > > than CD or how much less AB is than CD. > > > > > > 5. Finally, if a magnitude is only part of a unit, then we arrive at a > > > ratio of numbers, say AB : CD where AB and CD are multiples of the > > > unit. AB : CD now means the comparison of numbers AB and CD. When we > > > write AB/CD, it is called a fraction. > > > > > > So, in five steps I have derived the concept of number for you. There > > > is one thing left - what happens when you can't measure a magnitude > > > that is not a multiple of a unit and can't be expressed exactly using > > > any part of a unit? This is called an incommensurable magnitude and > > > the best you can do is provide an approximation such as 3.14159... or > > > 1.414..., etc. > > > > > > Euclid's Elements: > > > Definition of magnitude: Bk V. > > > My definition of magnitude is better than Euclid's because it is not > > > circular. Definition of number: Bk. VII > > > > > > The Axioms of Arithmetic: > > > > > > 1. The difference (or subtraction) of two numbers is that number which > > > describes how much the larger exceeds the smaller. > > > > > > Explanation: We start with the primitive operator of subtraction > > > (difference) which is '-'. We cannot do monkey things like 1-3 because > > > 1 is smaller than 3. > > > > That is not ruled out by your axiom. 1 - 3 is not forbidden by your > > axiom which simply refers to two number. > > > > 1 and 3 are two number. Subtraction is how much the larger exceed the > > smaller, so for 1 - 3, 3 is the larger, 1 is the smaller, 2 is how much > > the larger exceed the smaller so 1 - 3 = 2 > > > > > The smaller is subtracted from the bigger, like > > > this: 3 - 1 = 2. > > > > > > Besides, you *can't even begin* to do subtraction with the Peano rot > > > axioms!!! > > > > You have to define subtraction, which is done based upon the axioms and > > other operations which you define. > > > > > There is NO WAY you can say 1 - 3 in Peano's fartioms. :-) You have to > > > use '+' because it is the operator of the successor function. > > > > No .. its not. Though once addition is defined from peano you can > > express the successor using addition. Addition, subtraction and other > > operations can be derived from the successor. > > > > > Using my axioms, '-' is used in *every operation*. > > > > Not really a benefit. > > > > > 2. The difference of equal numbers is zero. > > > > > > Explanation: k - k = 0 > > > > That is fine > > > > > 3. The sum (or addition) of two numbers is that number whose > > > difference with either of the two numbers is either of the two > > > numbers. > > > > > > Explanation: m - n = d where m > n. So, n + d = m. > > > > So, lets take then numbers 2 and 3. We need to the look at either one > > or the other of those numbers. Lets take 3. We have that 6 - 3 = 3 and > > 3 is either of the numbers. So we get 2 + 3 = 6 > > > > > 4. The quotient (or division) of two numbers is that magnitude that > > > measures either number in terms of the other. > > > > Lets take 2 / 6. So we want the magnitude that measures either in terms > > of the other. 3 measure 6 in terms of 2. so 2 / 6 = 3 > > > > > Explanation: 2/3 measures 3. How? 3 - (2/3 + 2/3 + 2/3)=0 > > > or 2/3 + > > > 2/3 + 2/3 = 3 > > > > BAHAHAH .. 3 = 2/3 + 2/3 + 2/3 > > > > You're still a moron > > > > > since we defined addition in (3). > > > > > > 1/3 measures 2. How? 2 - (1/3+1/3+1/3+1/3+1/3+1/3) = 0. In this > > > case, 2 is measured by the reciprocal of 3. The axioms says "in terms > > > of the other". > > > > > > 5. If a unit is divided by a number into *equal* parts, then each of > > > these parts of a unit, is called the reciprocal of that number. > > > > You need to thank me for getting you to add the word "equal". I expect > > an acknowledgment for my contribution to improving this axiom > > > > > Explanation: 1/k + 1/k + +1/k (k times) = 1. > > > > > > 6. Division by zero is undefined. > > > > > > Explanation: Zero does not measure ANY other number except itself. > > > > > > 7. The product (or multiplication) of two numbers is the quotient of > > > either number with the reciprocal of the other. > > > > > > Explanation: m x n = m / (1/n) or n / (1/m) > > > > > > 8. The difference of any number and zero is the number. > > > > > > Observe that all the basic arithmetic operations are defined in terms > > > of difference. > > > > > > > Observe you updated your axioms with my correction, but they still are > > not correct. > > > > Observe your axions give 2 - 3 = 1, 2 + 3 - 6, 2 / 6 = 3
As long as you keep claiming that 2 - 3 = 1, you can't be helped. NONE of my axioms imply your stupidity. Rest of your ignorant rant ignored.