
Re: Infinity: The Story So Far
Posted:
Mar 2, 2014 12:26 AM


John Gabriel <thenewcalculus@gmail.com> wrote in news:b06c8941368e47109a2d15ae1d22d943@googlegroups.com:
> On Sunday, 2 March 2014 02:41:00 UTC+2, WizardOfOz wrote: >> John Gabriel <thenewcalculus@gmail.com> wrote in >> >> news:8ddd8dc8cfa94d959627bea41c0f9002@googlegroups.com: >> >> >> >> > This comment is intended as a service to those students who will >> >> > stumble on pile of trash called sci.math. >> >> > >> >> > I discuss the socalled 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 selfevident 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 socalled "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 13 >> > 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,
That is what your axioms say
> you can't be helped.
It is your axioms that need help
> NONE > of my axioms imply your stupidity.
Yes they do. I proved it > Rest of your ignorant rant ignored.
Ungrateful Coward
No thanks from you to me, I see, for me telling you that you had to specify equal parts in your repicrocal axiom, which you then changes as a result of me telling you
Of course, your reciprocal "axiom" only works one way .. from whole numbers to numbers that have one as a numerator.
Your axioms are flawed and pathetic. Just like you.

