Find out here:

https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics

On 7/5/2021 3:11 PM, Eram semper recta wrote:
> Find out here:

Shut up imbecile.

On Monday, 5 July 2021 at 18:11:30 UTC-4, Eram semper recta wrote:
> Find out here:
>
> https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics

Why is it important to understand the concept of number?

Because Mathematics is the science of measure and number.

On Tuesday, July 6, 2021 at 12:51:04 PM UTC+2, Eram semper recta wrote:
> On Monday, 5 July 2021 at 18:11:30 UTC-4, Eram semper recta wrote:
> > Find out here:
> >
> > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> Why is it important to understand the concept of number?
>
> Because Mathematics is the science of measure and number.

Mathematics is the science of patterns and abstraction.

How would you ascribe a number to the difference between radial displacement
as a function of angular displacement on the one hand and vertical displacement
as a function of horizontal displacement on the other hand (polar vs rectangular
coordinates)?
How would you ascribe a number to the distinction between a rotation symmetry
and a reflection symmetry in group theory?
Like what number would be associated with a reflection in the y-axis and how would that
relate to the number associated with a rotation of 180 degrees around the origin?

On Tuesday, 6 July 2021 at 09:28:40 UTC-4, sobriquet wrote:
> On Tuesday, July 6, 2021 at 12:51:04 PM UTC+2, Eram semper recta wrote:
> > On Monday, 5 July 2021 at 18:11:30 UTC-4, Eram semper recta wrote:
> > > Find out here:
> > >
> > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > Why is it important to understand the concept of number?
> >
> > Because Mathematics is the science of measure and number.
> Mathematics is the science of patterns and abstraction.

Nonsense.

:the science of numbers and their operations

https://www.merriam-webster.com/dictionary/mathematics

<drivel>

On Tuesday, July 6, 2021 at 6:19:18 PM UTC+2, Eram semper recta wrote:
> On Tuesday, 6 July 2021 at 09:28:40 UTC-4, sobriquet wrote:
> > On Tuesday, July 6, 2021 at 12:51:04 PM UTC+2, Eram semper recta wrote:
> > > On Monday, 5 July 2021 at 18:11:30 UTC-4, Eram semper recta wrote:
> > > > Find out here:
> > > >
> > > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > > Why is it important to understand the concept of number?
> > >
> > > Because Mathematics is the science of measure and number.
> > Mathematics is the science of patterns and abstraction.
> Nonsense.
>
> :the science of numbers and their operations
>
> https://www.merriam-webster.com/dictionary/mathematics
>
> <drivel>

You're having trouble reading?
M-W doesn't claim math to be just the science of numbers and their operations,
interrelations, combinations, generalizations, but also the science of
abstractions and of space (see SPACE entry 1 sense 7) configurations and
their structure, measurement, transformations, and generalizations.

So it's obviously about more than just numbers but rather about abstractions
and patterns in general.

On Tuesday, July 6, 2021 at 6:58:44 PM UTC+2, sobriquet wrote:
> On Tuesday, July 6, 2021 at 6:19:18 PM UTC+2, Eram semper recta wrote:
> > On Tuesday, 6 July 2021 at 09:28:40 UTC-4, sobriquet wrote:
> > > On Tuesday, July 6, 2021 at 12:51:04 PM UTC+2, Eram semper recta wrote:
> > > > On Monday, 5 July 2021 at 18:11:30 UTC-4, Eram semper recta wrote:
> > > > > Find out here:
> > > > >
> > > > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > > > Why is it important to understand the concept of number?
> > > >
> > > > Because Mathematics is the science of measure and number.
> > > Mathematics is the science of patterns and abstraction.
> > Nonsense.
> >
> > :the science of numbers and their operations
> >
> > https://www.merriam-webster.com/dictionary/mathematics
> >
> > <drivel>
> You're having trouble reading?
> M-W doesn't claim math to be just the science of numbers and their operations,
> interrelations, combinations, generalizations, but also the science of
> abstractions and of space (see SPACE entry 1 sense 7) configurations and
> their structure, measurement, transformations, and generalizations.
>
> So it's obviously about more than just numbers but rather about abstractions
> and patterns in general.

https://www.britannica.com/science/mathematics

mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative aspects of the life sciences.

On Monday, July 5, 2021 at 6:11:30 PM UTC-4, Eram semper recta wrote:
> Find out here:
>
> https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics

Of what use is your "definition" of a number, Troll Boy? You can't even establish the most elementary results of basic arithmetic (e.g. 2+2=4) in your goofy little system.

WARNING TO STUDENTS: Don't become a victim of JG's fake math

JG here claims to have a discovered as shortcut to mastering calculus without using limits. Unfortunately for him, this means he has no workable a definition of the derivative of a function. It blows up for functions as simple f(x)=|x|. Or even f(x)=0. As a result, he has had to ban 0, negative numbers and instantaneous rates of change rendering his goofy little system quite useless. What a moron!

Forget calculus. JG has also banned all axioms because he cannot even derive the most elementary results of basic arithmetic, e.g. 2+2=4. Such results require the use of axioms, so he must figure he's now off the hook. Again, what a moron!

Even at his advanced age (60+?), John Gabriel is STILL struggling with basic, elementary-school arithmetic. As he has repeatedly posted here:

"There are no points on a line."
--April 12, 2021

"Pi is NOT a number of ANY kind!"
--July 10, 2020

"1/2 not equal to 2/4"
--October 22, 2017

“1/3 does NOT mean 1 divided by 3 and never has meant that”
-- February 8, 2015

"3 =< 4 is nonsense.”
--October 28, 2017

"Zero is not a number."
-- Dec. 2, 2019

"0 is not required at all in mathematics, just like negative numbers."
-- Jan. 4, 2017

“There is no such thing as an empty set.”
--Oct. 4, 2019

“3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)
--Oct. 22, 2019

No math genius our JG, though he actually lists his job title as “mathematician” at Linkedin.com. Apparently, they do not verify your credentials.

Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog a http://www.dcproof.wordpress.com

On Tuesday, 6 July 2021 at 12:58:44 UTC-4, sobriquet wrote:
> On Tuesday, July 6, 2021 at 6:19:18 PM UTC+2, Eram semper recta wrote:
> > On Tuesday, 6 July 2021 at 09:28:40 UTC-4, sobriquet wrote:
> > > On Tuesday, July 6, 2021 at 12:51:04 PM UTC+2, Eram semper recta wrote:
> > > > On Monday, 5 July 2021 at 18:11:30 UTC-4, Eram semper recta wrote:
> > > > > Find out here:
> > > > >
> > > > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > > > Why is it important to understand the concept of number?
> > > >
> > > > Because Mathematics is the science of measure and number.
> > > Mathematics is the science of patterns and abstraction.
> > Nonsense.
> >
> > :the science of numbers and their operations
> >
> > https://www.merriam-webster.com/dictionary/mathematics
> >
> > <drivel>
> You're having trouble reading?

LOL. If I were, let me tell you that your problems are much bigger because you have trouble thinking!

Mathematics is the SCIENCE or measure and number.

THIS AND NOTHING ELSE.

<drivel>

On Tuesday, July 6, 2021 at 7:48:21 PM UTC+1, Eram semper recta wrote:

"Mathematics is the SCIENCE or measure and number...THIS AND NOTHING ELSE. "

Not according to the current community of mathematicians, not according to mathematicians of the past 100 years (well, more actually), not according to philosophers of mathematics and not according to the very dictionary that you cited, either without reading properly or just hoped no one else would.. Honestly, can you now understand why I am more inclined to believe your IQ is around 115 rather than over 160? The intellectual entropy of your posts continues to increase Sir.

In all seriousness: take some time away from sci.math (a month, say). Take advantage of the summer sunshine, maybe try out some alternative hobbies. I believe you were thinking about music recently on your YouTube channel, so maybe that's a place to start. This kind of pointless self-pwnage can't be doing you any good and serves no useful purpose for anyone else either. Leave the pointless intellectual self-destruction to Archimedes Plutonium who is probably far too gone to help and only has the prospect of being logged in some future internet historian's journal entry to look forward to.

Have a Wonderful Day
QB

Remain Calm and Keep Loving Real Analysis
[Recommended Book of the Day: A First Course in Probability, 6e, by Sheldon Ross (no relation)]

On Tuesday, 6 July 2021 at 15:14:46 UTC-4, Quantum Babbling aka ross.pro...@gmx.com wrote:

You obviously have a lot of idle time on your hands, but I am going to chop them off (not literally).

You need to shut the fuck up because when I find out who you are, I am going to do a lot of damage to you! I shall contact your boss and get you fired, you vile piece of shit. It will not go well for you, so I am warning you: fuck off and stop pestering me. Nothing you say has any value. I piss and shit on your every word, you vile Limey bastard. An ape like you has nothing to say to a genius. You are a NOBODY.

If I find out who you are, I am going to fuck you pretty well and I am working on it!!! Prof. Gilbert Strang, the fucking felon from MIT didn't think I could until I did. Same fate awaits you, dog!!! I would rip your eyes out and shove them up your arse if I could get away with it. LMAO.

Now do the right thing and fuck off!

On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> Find out here:
>
> https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics

I think the concept number is a bit fuzzy and it can mean lots of things in different
(mathematical) contexts. It seems silly to try to come up with some ultimate
interpretation of the concept of a number and arguing that pi isn't a number.
It's a fascinating topic though, and more generally math as the backbone of science.

Science has achieved some remarkable conceptual progress, judging from the
technological innovations it has enabled us to come up with, so the math
can't be completely flawed, otherwise math wouldn't provide a reasonably
solid conceptual foundation for science.

The most profound scientific realizations so far seem to be quantum field theory
and general relativity at the moment and they appear to go beyond numbers in
the sense that they also deal with stuff like group theory as abstract structures
where different phenomena that can be observed, like photons and electrons seem
to obey certain principles from group theory.

https://en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics#Unitary_groups_in_quantum_field_theory

Like the way some things have to be rotated around twice to match up with
themselves, whereas our everyday intuition tends to deal with things that match up
with themselves after a single full rotation. And then there are aspects like entanglement
and superposition and I guess these kind of work like primitive concepts or the very
conceptual building blocks for understanding reality that kind of render earlier
conceptualizations of the fundamental constituent building blocks of reality redundant
or outdated.
Since many earlier ideas originated in a time when we had a lot less empirical knowledge
about the world and back then we came up with ideas that made sense in that context but
that seem kind of outdated in the context of contemporary science.
If we had to start all over again from scratch while retaining all the observations and
experiments done so far, we would probably come up with an entirely different conceptual
framework. Our concepts have to fit the observations and outcomes of empirical science
and not the other way around.

We know from history that humans have come up with very clumsy conceptualizations
of numbers like Roman numerals that make arithmetic needlessly complicated, so it
stands to reason that our current conceptualization of numbers is probably far from
optimal as well.
We also can see that there are very different ways to go about abstract algebra (where
algebra is understood as an abstraction of arithmetic) instead of the traditional
linear algebra approach, like geometric algebra that seem way more suitable to
handle advanced physics and computer graphics, where we have a unified
conceptual framework that handles a wide range of applications in an elegant
way.

https://www.youtube.com/watch?v=tX4H_ctggYo

On Tuesday, 6 July 2021 at 19:47:47 UTC-4, sobriquet wrote:
> On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> > Find out here:
> >
> > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> I think the concept number is a bit fuzzy and it can mean lots of things in different
> (mathematical) contexts.

Your statement (wrong as it is!) confirms my long time claim that mainstream academics have never understood the concept of number. It is by no means fuzzy and has a precise meaning:

A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.

That definition encompasses the RATIONAL NUMBERS. Anything else is NOT a number.

> It seems silly to try to come up with some ultimate
> interpretation of the concept of a number and arguing that pi isn't a number.

Does it really? Chuckle.

> It's a fascinating topic though, and more generally math as the backbone of science.

How can a "silly topic" be fascinating? Do you enjoy contradicting yourself?

NOTHING we have used in STEM relies on anything but the certainty of RATIONAL NUMBERS. We have never used "real numbers" because they don't exist as well-formed concepts, only as absurdities in your dysfunctional mind.

<drivel>

On Tuesday, 6 July 2021 at 19:47:47 UTC-4, sobriquet wrote:
> On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> > Find out here:
> >
> > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics

Epping or Penrith? If Epping, have you been to the Art Gallery there?

On Wednesday, July 7, 2021 at 1:58:00 PM UTC+2, Eram semper recta wrote:
> On Tuesday, 6 July 2021 at 19:47:47 UTC-4, sobriquet wrote:
> > On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> > > Find out here:
> > >
> > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > I think the concept number is a bit fuzzy and it can mean lots of things in different
> > (mathematical) contexts.
> Your statement (wrong as it is!) confirms my long time claim that mainstream academics have never understood the concept of number. It is by no means fuzzy and has a precise meaning:
>
> A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.
>
> That definition encompasses the RATIONAL NUMBERS. Anything else is NOT a number.

I doubt we would have had as much scientific progress as we had if we would
accept such an idiotic definition. Number systems are like those Russian dolls where you open
them up and find a Russian doll inside. Working with numbers naturally promotes thinking outside
of the box, as operations on numbers can yield results outside the previously assumed range
(like subtraction of natural numbers yielding negative numbers and
taking square roots yielding irrational or complex numbers).

Even bees have numbers.. they use polar coordinates to tell their fellow bees where they can find
nectar (that is, in what direction they have to fly and how far).

> > It seems silly to try to come up with some ultimate
> > interpretation of the concept of a number and arguing that pi isn't a number.
> Does it really? Chuckle.
> > It's a fascinating topic though, and more generally math as the backbone of science.
> How can a "silly topic" be fascinating? Do you enjoy contradicting yourself?

Your approach to the topic of numbers is silly, while the topic of numbers itself is fascinating.
I can see how people originally were shocked to find out that irrational numbers exist, as one
might initially hope to have stumbled across a beautiful self-contained system with an infinite
bunch of rational numbers and then to find out that even an infinite number of rational numbers
is not enough to cover all possible locations on the number line.

>
> NOTHING we have used in STEM relies on anything but the certainty of RATIONAL NUMBERS. We have never used "real numbers" because they don't exist as well-formed concepts, only as absurdities in your dysfunctional mind.
>
> <drivel>

Nonsense.. you have no evidence whatsoever so substantiate such ludicrous claims.

On Wednesday, July 7, 2021 at 2:18:54 PM UTC+2, Eram semper recta wrote:
> On Tuesday, 6 July 2021 at 19:47:47 UTC-4, sobriquet wrote:
> > On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> > > Find out here:
> > >
> > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> Epping or Penrith? If Epping, have you been to the Art Gallery there?

I'm in Utrecht.. but I prefer collecting digital art rather than visiting art galleries.

On Wednesday, 7 July 2021 at 09:13:09 UTC-4, sobriquet wrote:
> On Wednesday, July 7, 2021 at 1:58:00 PM UTC+2, Eram semper recta wrote:
> > On Tuesday, 6 July 2021 at 19:47:47 UTC-4, sobriquet wrote:
> > > On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> > > > Find out here:
> > > >
> > > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > > I think the concept number is a bit fuzzy and it can mean lots of things in different
> > > (mathematical) contexts.
> > Your statement (wrong as it is!) confirms my long time claim that mainstream academics have never understood the concept of number. It is by no means fuzzy and has a precise meaning:
> >
> > A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.
> >
> > That definition encompasses the RATIONAL NUMBERS. Anything else is NOT a number.
> I doubt we would have had as much scientific progress as we had if we would
> accept such an idiotic definition.

Only an idiot would make such a statement.

> Number systems are like those Russian dolls where you open
> them up and find a Russian doll inside.

Chuckle. On the contrary, that's what set theory is like. Sound number theory is not a Matryoshka doll scheme.

> Working with numbers naturally promotes thinking outside
> of the box, as operations on numbers can yield results outside the previously assumed range
> (like subtraction of natural numbers yielding negative numbers and
> taking square roots yielding irrational or complex numbers).
>
> Even bees have numbers.. they use polar coordinates to tell their fellow bees where they can find
> nectar (that is, in what direction they have to fly and how far).
> > > It seems silly to try to come up with some ultimate
> > > interpretation of the concept of a number and arguing that pi isn't a number.
> > Does it really? Chuckle.
> > > It's a fascinating topic though, and more generally math as the backbone of science.
> > How can a "silly topic" be fascinating? Do you enjoy contradicting yourself?
> Your approach to the topic of numbers is silly, while the topic of numbers itself is fascinating.
> I can see how people originally were shocked to find out that irrational numbers exist, as one
> might initially hope to have stumbled across a beautiful self-contained system with an infinite
> bunch of rational numbers and then to find out that even an infinite number of rational numbers
> is not enough to cover all possible locations on the number line.
> >
> > NOTHING we have used in STEM relies on anything but the certainty of RATIONAL NUMBERS. We have never used "real numbers" because they don't exist as well-formed concepts, only as absurdities in your dysfunctional mind.
> >
> > <drivel>
> Nonsense.. you have no evidence whatsoever so substantiate such ludicrous claims.

What you write is nonsense. There is no such thing as a real number line, but how can you know? You're obviously an idiot given your comments.

Eram semper recta <thenewcalculus@gmail.com> wrote:
> On Wednesday, 7 July 2021 at 09:13:09 UTC-4, sobriquet wrote:
>> On Wednesday, July 7, 2021 at 1:58:00 PM UTC+2, Eram semper recta wrote:

[ .... ]

>> > A number is a NAME given to a MEASURE that describes a MAGNITUDE or
>> > SIZE.

>> > That definition encompasses the RATIONAL NUMBERS. Anything else is
>> > NOT a number.
>> I doubt we would have had as much scientific progress as we had if we
>> would accept such an idiotic definition.

> Only an idiot would make such a statement.

You, John, are the pusher of that ridiculous "definition" of numbers,
complete with ridiculous capitalisation. It may have been OK in the
late bronze age, but it's just a ridiculous mash of meaningless words
nowadays.

[ .... ]

>> > NOTHING we have used in STEM relies on anything but the certainty
>> > of RATIONAL NUMBERS. We have never used "real numbers" because they
>> > don't exist as well-formed concepts, only as absurdities in your
>> > dysfunctional mind.

That is just plain wrong, John. Much in science and technology uses
real numbers and complex numbers.

>> > <drivel>
>> Nonsense.. you have no evidence whatsoever so substantiate such
>> ludicrous claims.

> What you write is nonsense. There is no such thing as a real number
> line, but how can you know? You're obviously an idiot given your
> comments.

John, I advise you to stop making such extravagant statements. As I
keep having to point out to you, you don't understand what it means for
something mathematical to exist or not to exist.

As it turns out, the real numbers most emphatically do exist, along with
their picturing as the real line.

--
Alan Mackenzie (Nuremberg, Germany).

On Monday, 5 July 2021 at 18:11:30 UTC-4, Eram semper recta wrote:
> Find out here:
>
> https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics

Students:

Since mathematics is about measure and number, shouldn't you gain a profound understanding about the meaning of number?

Of course, you should! The concept of number is the most important concept in mathematics. You cannot understand mathematics unless you master the concept of number.

On Wednesday, July 7, 2021 at 5:08:48 PM UTC+2, Eram semper recta wrote:
> On Wednesday, 7 July 2021 at 09:13:09 UTC-4, sobriquet wrote:
> > On Wednesday, July 7, 2021 at 1:58:00 PM UTC+2, Eram semper recta wrote:
> > > On Tuesday, 6 July 2021 at 19:47:47 UTC-4, sobriquet wrote:
> > > > On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> > > > > Find out here:
> > > > >
> > > > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > > > I think the concept number is a bit fuzzy and it can mean lots of things in different
> > > > (mathematical) contexts.
> > > Your statement (wrong as it is!) confirms my long time claim that mainstream academics have never understood the concept of number. It is by no means fuzzy and has a precise meaning:
> > >
> > > A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.
> > >
> > > That definition encompasses the RATIONAL NUMBERS. Anything else is NOT a number.
> > I doubt we would have had as much scientific progress as we had if we would
> > accept such an idiotic definition.
> Only an idiot would make such a statement.

I might be an idiot, but at least I'm aware of it!

Seriously though, why would anyone accept your vacuous claims?

> > Number systems are like those Russian dolls where you open
> > them up and find a Russian doll inside.
> Chuckle. On the contrary, that's what set theory is like. Sound number theory is not a Matryoshka doll scheme.

Even your system is, though it's not many layers deep. The integers (or natural numbers if you
want to avoid negative numbers) are embedded in the rational numbers. So if you look inside
the outer Russian doll (the rational number system), you find an inner Russian doll (the
natural number system).
The natural number system is the intuitive system for counting discrete things (like how many sides
a regular polygon has), while the rational number system is the intuitive system for continuous
quantities like distances or angles, since we can approximate a quantity by splitting up some unit
quantity into successively smaller portions and considering an aggregation of such portions.

> > Working with numbers naturally promotes thinking outside
> > of the box, as operations on numbers can yield results outside the previously assumed range
> > (like subtraction of natural numbers yielding negative numbers and
> > taking square roots yielding irrational or complex numbers).
> >
> > Even bees have numbers.. they use polar coordinates to tell their fellow bees where they can find
> > nectar (that is, in what direction they have to fly and how far).
> > > > It seems silly to try to come up with some ultimate
> > > > interpretation of the concept of a number and arguing that pi isn't a number.
> > > Does it really? Chuckle.
> > > > It's a fascinating topic though, and more generally math as the backbone of science.
> > > How can a "silly topic" be fascinating? Do you enjoy contradicting yourself?
> > Your approach to the topic of numbers is silly, while the topic of numbers itself is fascinating.
> > I can see how people originally were shocked to find out that irrational numbers exist, as one
> > might initially hope to have stumbled across a beautiful self-contained system with an infinite
> > bunch of rational numbers and then to find out that even an infinite number of rational numbers
> > is not enough to cover all possible locations on the number line.
> > >
> > > NOTHING we have used in STEM relies on anything but the certainty of RATIONAL NUMBERS. We have never used "real numbers" because they don't exist as well-formed concepts, only as absurdities in your dysfunctional mind.
> > >
> > > <drivel>
> > Nonsense.. you have no evidence whatsoever so substantiate such ludicrous claims.
> What you write is nonsense. There is no such thing as a real number line, but how can you know? You're obviously an idiot given your comments.

The real number line exists in the same conceptual space where rational numbers exist.
How can you know that a rational number exists? You can't see, hear, smell, taste or
touch it, you can't collide rational numbers together to see what constituents it
consists of (like you can do with protons or other building blocks of matter).

On Wednesday, 7 July 2021 at 12:07:49 UTC-4, sobriquet wrote:
> On Wednesday, July 7, 2021 at 5:08:48 PM UTC+2, Eram semper recta wrote:
> > On Wednesday, 7 July 2021 at 09:13:09 UTC-4, sobriquet wrote:
> > > On Wednesday, July 7, 2021 at 1:58:00 PM UTC+2, Eram semper recta wrote:
> > > > On Tuesday, 6 July 2021 at 19:47:47 UTC-4, sobriquet wrote:
> > > > > On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> > > > > > Find out here:
> > > > > >
> > > > > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > > > > I think the concept number is a bit fuzzy and it can mean lots of things in different
> > > > > (mathematical) contexts.
> > > > Your statement (wrong as it is!) confirms my long time claim that mainstream academics have never understood the concept of number. It is by no means fuzzy and has a precise meaning:
> > > >
> > > > A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.
> > > >
> > > > That definition encompasses the RATIONAL NUMBERS. Anything else is NOT a number.
> > > I doubt we would have had as much scientific progress as we had if we would
> > > accept such an idiotic definition.
> > Only an idiot would make such a statement.
> I might be an idiot, but at least I'm aware of it!

Idiots are usually not aware that they are idiots. :)

>
> Seriously though, why would anyone accept your vacuous claims?

I have no vacuous claims, so perhaps you might clarify? There is nothing vacuous about:

A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.

Only an idiot can state that the above well-formed definition of number is vacuous. More than likely you are thinking of the vast spaces in your brain? Chuckle.

Assertions are worthless.

> > > Number systems are like those Russian dolls where you open
> > > them up and find a Russian doll inside.
> > Chuckle. On the contrary, that's what set theory is like. Sound number theory is not a Matryoshka doll scheme.
> Even your system is, though it's not many layers deep.

False. I have NO SYTEM. System is a word that uneducated morons like you and your fellow idiots in the mainstream love to use. It took 6 books of the Elements before the abstract concept of number is introduced in book 7. Hm. That sounds like more layers than any of the bullshit you have in set theory in which "set" is never defined. LMAO.

> The integers (or natural numbers if you
> want to avoid negative numbers) are embedded in the rational numbers.

Integers and natural numbers ARE **rational numbers** which came before these.

> So if you look inside
> the outer Russian doll (the rational number system), you find an inner Russian doll (the
> natural number system).
> The natural number system is the intuitive system

I stop here. Anyone using the word intuitive or intuition is an utter imbecile who is not worth educating.

<drivel>

Learn what it means to construct a number line:

https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc

There is NO real number line because there is no such thing as a "real number".

Is a matrix a number, or a collection of numbers?
Similarly, is a complex number a number, or a pair of numbers?

--
Basil Jet recently enjoyed listening to
2015 - Exploitation - Róisín Murphy

On Wednesday, July 7, 2021 at 6:30:41 PM UTC+2, Eram semper recta wrote:
> On Wednesday, 7 July 2021 at 12:07:49 UTC-4, sobriquet wrote:
> > On Wednesday, July 7, 2021 at 5:08:48 PM UTC+2, Eram semper recta wrote:
> > > On Wednesday, 7 July 2021 at 09:13:09 UTC-4, sobriquet wrote:
> > > > On Wednesday, July 7, 2021 at 1:58:00 PM UTC+2, Eram semper recta wrote:
> > > > > On Tuesday, 6 July 2021 at 19:47:47 UTC-4, sobriquet wrote:
> > > > > > On Tuesday, July 6, 2021 at 12:11:30 AM UTC+2, Eram semper recta wrote:
> > > > > > > Find out here:
> > > > > > >
> > > > > > > https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics
> > > > > > I think the concept number is a bit fuzzy and it can mean lots of things in different
> > > > > > (mathematical) contexts.
> > > > > Your statement (wrong as it is!) confirms my long time claim that mainstream academics have never understood the concept of number. It is by no means fuzzy and has a precise meaning:
> > > > >
> > > > > A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.
> > > > >
> > > > > That definition encompasses the RATIONAL NUMBERS. Anything else is NOT a number.
> > > > I doubt we would have had as much scientific progress as we had if we would
> > > > accept such an idiotic definition.
> > > Only an idiot would make such a statement.
> > I might be an idiot, but at least I'm aware of it!
> Idiots are usually not aware that they are idiots. :)
> >
> > Seriously though, why would anyone accept your vacuous claims?
> I have no vacuous claims, so perhaps you might clarify? There is nothing vacuous about:
> A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.
> Only an idiot can state that the above well-formed definition of number is vacuous. More than likely you are thinking of the vast spaces in your brain? Chuckle.

How do you expect people to understand what you're talking about? You expect them to look up
these words "NAME", "MEASURE", "MAGNITUDE" and "SIZE" in a dictionary and work out what
you could possibly mean by them (given that use typically have multiple connotations)?
Unless you actually pin down the exact meaning of terms you are using, the meaning is up for
grabs and different people will interpret it in different ways.
Euclid wasn't very good at that either with cryptic statements like "A point is that which has no part."
or "A line is breadthless length.".

>
> Assertions are worthless.
> > > > Number systems are like those Russian dolls where you open
> > > > them up and find a Russian doll inside.
> > > Chuckle. On the contrary, that's what set theory is like. Sound number theory is not a Matryoshka doll scheme.
> > Even your system is, though it's not many layers deep.
> False. I have NO SYTEM. System is a word that uneducated morons like you and your fellow idiots in the mainstream love to use. It took 6 books of the Elements before the abstract concept of number is introduced in book 7. Hm. That sounds like more layers than any of the bullshit you have in set theory in which "set" is never defined. LMAO.

You're using the Hindu-Arabic numeral system, whether you're aware of it or not.

https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system

> > The integers (or natural numbers if you
> > want to avoid negative numbers) are embedded in the rational numbers.
> Integers and natural numbers ARE **rational numbers** which came before these.
> > So if you look inside
> > the outer Russian doll (the rational number system), you find an inner Russian doll (the
> > natural number system).
> > The natural number system is the intuitive system
> I stop here. Anyone using the word intuitive or intuition is an utter imbecile who is not worth educating.

Intuition is a universal human concept.

>
> <drivel>
>
> Learn what it means to construct a number line:
>
> https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc
>
> There is NO real number line because there is no such thing as a "real number".

So your rational number line has holes in it (like at the square-root of 2 or pi)?

On Wednesday, July 7, 2021 at 7:01:13 PM UTC+2, sobriquet wrote:
>[..]
> How do you expect people to understand what you're talking about? You expect them to look up
> these words "NAME", "MEASURE", "MAGNITUDE" and "SIZE" in a dictionary and work out what
> you could possibly mean by them (given that words typically have multiple connotations)?
>[..]

Basil Jet <basil@spamspamspam.com> wrote:

> Is a matrix a number, or a collection of numbers?

Yes. Matrices of a particular square size over a field satisfy the ring
axioms. Matrices are not typically regarded as numbers.

> Similarly, is a complex number a number, or a pair of numbers?

Also yes. A complex number is indeed a number.

But so what? Matrices and complex numbers are what they are, and what
they are is independent of the labels one gives them. "Number" has
several shades of meaning, and insisting that something "is" a number is
just giving fuel to those who love to argue endlessly about words whilst
imagining at the same time they are being very profound.

> --
> Basil Jet recently enjoyed listening to
> 2015 - Exploitation - Róisín Murphy

--
Alan Mackenzie (Nuremberg, Germany).