Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Wizard-Of-Oz Posts: 404 Registered: 12/28/13
Re: Infinity: The Story So Far
Posted: Mar 2, 2014 12:26 AM
 Plain Text Reply

John Gabriel <thenewcalculus@gmail.com> wrote in
news:b06c8941-368e-4710-9a2d-15ae1d22d943@googlegroups.com:

> On Sunday, 2 March 2014 02:41:00 UTC+2, Wizard-Of-Oz wrote:
>> John Gabriel <thenewcalculus@gmail.com> wrote in
>>
>> news:8ddd8dc8-cfa9-4d95-9627-bea41c0f9002@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 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,

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.

Date Subject Author
2/25/14 Dan Christensen
2/25/14 Brian Q. Hutchings
2/25/14 ross.finlayson@gmail.com
2/25/14 ross.finlayson@gmail.com
2/26/14 Leo Sgouros
2/26/14 ross.finlayson@gmail.com
2/26/14 William Elliot
3/1/14 Dan Christensen
3/2/14 Brian Q. Hutchings
2/26/14 thenewcalculus@gmail.com
2/26/14 Dan Christensen
2/26/14 thenewcalculus@gmail.com
2/26/14 Dan Christensen
2/26/14 Virgil
2/26/14 Dan Christensen
2/26/14 Martin Shobe
2/26/14 ross.finlayson@gmail.com
2/27/14 Dan Christensen
2/27/14 Martin Shobe
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Virgil
2/26/14 thenewcalculus@gmail.com
2/26/14 Dan Christensen
2/26/14 thenewcalculus@gmail.com
2/26/14 Dan Christensen
2/26/14 thenewcalculus@gmail.com
2/26/14 Dan Christensen
2/26/14 Brian Q. Hutchings
2/26/14 mueckenh@rz.fh-augsburg.de
2/26/14 Dan Christensen
2/26/14 mueckenh@rz.fh-augsburg.de
2/26/14 Dan Christensen
2/26/14 Brian Q. Hutchings
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Virgil
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Dan Christensen
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Dan Christensen
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 fom
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Tanu R.
2/27/14 Tanu R.
2/28/14 Virgil
2/27/14 Virgil
2/27/14 Tanu R.
2/27/14 fom
2/27/14 thenewcalculus@gmail.com
2/28/14 Virgil
2/28/14 mueckenh@rz.fh-augsburg.de
2/28/14 Virgil
2/28/14 mueckenh@rz.fh-augsburg.de
2/28/14 Virgil
2/28/14 fom
2/27/14 Virgil
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Tanu R.
2/27/14 thenewcalculus@gmail.com
2/27/14 Virgil
2/26/14 Virgil
2/26/14 mueckenh@rz.fh-augsburg.de
2/26/14 Virgil
2/26/14 Dan Christensen
2/26/14 fom
2/26/14 mueckenh@rz.fh-augsburg.de
2/26/14 fom
2/26/14 Dan Christensen
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Virgil
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Virgil
2/27/14 Dan Christensen
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 fom
2/27/14 Peter Percival
2/27/14 fom
2/27/14 Peter Percival
2/27/14 fom
2/27/14 thenewcalculus@gmail.com
4/7/14 Aatu Koskensilta
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Virgil
2/26/14 Virgil
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Virgil
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Virgil
2/26/14 thenewcalculus@gmail.com
2/26/14 Brian Q. Hutchings
2/26/14 Virgil
2/26/14 mueckenh@rz.fh-augsburg.de
2/26/14 Virgil
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Virgil
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Virgil
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Tanu R.
2/26/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Martin Shobe
2/27/14 thenewcalculus@gmail.com
2/27/14 Martin Shobe
2/27/14 thenewcalculus@gmail.com
2/27/14 thenewcalculus@gmail.com
2/27/14 thenewcalculus@gmail.com
2/27/14 Martin Shobe
2/27/14 thenewcalculus@gmail.com
2/27/14 Martin Shobe
2/27/14 thenewcalculus@gmail.com
2/27/14 Martin Shobe
2/27/14 thenewcalculus@gmail.com
2/28/14 Martin Shobe
2/28/14 thenewcalculus@gmail.com
2/28/14 Martin Shobe
2/28/14 John Gabriel
2/28/14 Martin Shobe
2/28/14 John Gabriel
2/28/14 Sal Honda
2/27/14 Wizard-Of-Oz
2/27/14 fom
2/27/14 thenewcalculus@gmail.com
2/27/14 fom
2/27/14 mueckenh@rz.fh-augsburg.de
2/27/14 Wizard-Of-Oz
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/28/14 Wizard-Of-Oz
2/28/14 thenewcalculus@gmail.com
2/28/14 Wizard-Of-Oz
2/28/14 Dan Christensen
2/28/14 Wizard-Of-Oz
2/28/14 Wizard-Of-Oz
2/28/14 Wizard-Of-Oz
2/28/14 thenewcalculus@gmail.com
2/28/14 Wizard-Of-Oz
2/27/14 thenewcalculus@gmail.com
2/27/14 thenewcalculus@gmail.com
2/27/14 thenewcalculus@gmail.com
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/27/14 Dan Christensen
2/28/14 thenewcalculus@gmail.com
2/28/14 Dan Christensen
2/27/14 thenewcalculus@gmail.com
2/28/14 Dan Christensen
2/28/14 thenewcalculus@gmail.com
2/28/14 Dan Christensen
2/28/14 John Gabriel
2/28/14 Dan Christensen
2/28/14 John Gabriel
2/28/14 fom
2/28/14 John Gabriel
2/28/14 fom
2/28/14 John Gabriel
2/28/14 Dan Christensen
2/28/14 Wizard-Of-Oz
2/28/14 John Gabriel
2/28/14 Harman Kardan
2/28/14 John Gabriel
2/28/14 Wizard-Of-Oz
2/28/14 Johnny Oiler
3/1/14 thenewcalculus@gmail.com
3/1/14 Dan Christensen
3/1/14 thenewcalculus@gmail.com
3/1/14 Dan Christensen
3/1/14 thenewcalculus@gmail.com
3/1/14 Dan Christensen
3/1/14 thenewcalculus@gmail.com
3/1/14 Dan Christensen
3/1/14 thenewcalculus@gmail.com
3/2/14 Wizard-Of-Oz
3/1/14 Dan Christensen
3/2/14 Dan Christensen
3/1/14 Wizard-Of-Oz
3/1/14 thenewcalculus@gmail.com
3/2/14 Wizard-Of-Oz
3/1/14 thenewcalculus@gmail.com
3/1/14 thenewcalculus@gmail.com
3/2/14 Dan Christensen
3/2/14 thenewcalculus@gmail.com
3/2/14 Dan Christensen
3/2/14 John Gabriel
3/2/14 Wizard-Of-Oz
3/2/14 Dan Christensen
3/2/14 thenewcalculus@gmail.com
3/2/14 Dan Christensen
3/2/14 thenewcalculus@gmail.com
3/2/14 Dan Christensen
3/2/14 thenewcalculus@gmail.com
3/2/14 Dan Christensen
3/2/14 John Gabriel
3/2/14 Dan Christensen
3/3/14 John Gabriel
3/3/14 Dan Christensen
3/3/14 Wizard-Of-Oz
3/3/14 thenewcalculus@gmail.com
3/3/14 Virgil
3/2/14 Wizard-Of-Oz
3/2/14 thenewcalculus@gmail.com
3/2/14 JÃÂ¼rgen R.
3/2/14 thenewcalculus@gmail.com
3/3/14 New Balance
3/2/14 Wizard-Of-Oz
3/2/14 New Balance
3/4/14 thenewcalculus@gmail.com
3/4/14 thenewcalculus@gmail.com
3/4/14 Dan Christensen
3/4/14 thenewcalculus@gmail.com
3/4/14 Dan Christensen
3/4/14 Dan Christensen
3/4/14 Dan Christensen
3/5/14 thenewcalculus@gmail.com
3/5/14 Dan Christensen
3/5/14 thenewcalculus@gmail.com
3/4/14 ross.finlayson@gmail.com
3/5/14 ross.finlayson@gmail.com
3/5/14 Dan Christensen
3/5/14 ross.finlayson@gmail.com
3/5/14 Brian Q. Hutchings
3/5/14 Dan Christensen
3/5/14 thenewcalculus@gmail.com
3/5/14 Dan Christensen
3/5/14 thenewcalculus@gmail.com
3/5/14 Dan Christensen
3/5/14 Dan Christensen
3/5/14 thenewcalculus@gmail.com
3/5/14 Dan Christensen
3/5/14 thenewcalculus@gmail.com
3/5/14 Dan Christensen
3/5/14 thenewcalculus@gmail.com
3/5/14 Dan Christensen
3/6/14 thenewcalculus@gmail.com
3/6/14 Dan Christensen
3/6/14 Dan Christensen
3/6/14 thenewcalculus@gmail.com
3/5/14 YBM
3/6/14 New Balance
3/6/14 thenewcalculus@gmail.com
3/6/14 Brian Q. Hutchings
3/5/14 thenewcalculus@gmail.com
3/5/14 Dan Christensen
3/5/14 thenewcalculus@gmail.com
3/5/14 Dan Christensen
3/5/14 Peter Percival
3/5/14 thenewcalculus@gmail.com
3/5/14 Martin Shobe
3/5/14 Wizard-Of-Oz
3/5/14 Wizard-Of-Oz
3/5/14 Wizard-Of-Oz
3/5/14 thenewcalculus@gmail.com
3/6/14 Dan Christensen
3/6/14 thenewcalculus@gmail.com
3/6/14 thenewcalculus@gmail.com
3/11/14 thenewcalculus@gmail.com
3/11/14 Wizard-Of-Oz
3/11/14 Martin Shobe
3/11/14 thenewcalculus@gmail.com
3/11/14 Martin Shobe
3/11/14 thenewcalculus@gmail.com
3/11/14 thenewcalculus@gmail.com
3/11/14 Martin Shobe
3/11/14 thenewcalculus@gmail.com
3/11/14 thenewcalculus@gmail.com
3/11/14 Martin Shobe
3/12/14 thenewcalculus@gmail.com
3/12/14 Martin Shobe
3/12/14 ross.finlayson@gmail.com

© The Math Forum at NCTM 1994-2018. All Rights Reserved.