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Topic: Infinity: The Story So Far
Replies: 298   Last Post: Apr 7, 2014 7:30 AM

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 thenewcalculus@gmail.com Posts: 1,361 Registered: 11/1/13
Re: Infinity: The Story So Far
Posted: Mar 1, 2014 11:15 PM

On Sunday, 2 March 2014 02:41:00 UTC+2, Wizard-Of-Oz wrote:
> John Gabriel <thenewcalculus@gmail.com> wrote in
>
>
>
>

> > 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.
>
> >
>
>
> > (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
>
>
> 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.

Date Subject Author
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