1/3*3=1
but .333 does not equal 1/3
Those are different in quantity
and representation.
Calculus shows the difference
by what builds sizes of infinity
instead.

Mitchell Raemsch

søndag 12. desember 2021 kl. 21:45:07 UTC+1 skrev mitchr...@gmail.com:
> 1/3*3=1
> but .333 does not equal 1/3
> Those are different in quantity
> and representation.
> Calculus shows the difference
> by what builds sizes of infinity
> instead.
>
> Mitchell Raemsch
..333 is not equal to 1/3. That is true! But 0.333... is equal to 1/3.
KON

On Sunday, December 12, 2021 at 1:22:35 PM UTC-8, konyberg wrote:
> søndag 12. desember 2021 kl. 21:45:07 UTC+1 skrev mitchr...@gmail.com:
> > 1/3*3=1
> > but .333 does not equal 1/3
> > Those are different in quantity
> > and representation.
> > Calculus shows the difference
> > by what builds sizes of infinity
> > instead.
> >
> > Mitchell Raemsch
> .333 is not equal to 1/3. That is true! But 0.333... is equal to 1/3.
> KON

You can't have it both ways. They are both different...
in either order...

mitchr...@gmail.com <mitchrae3323@gmail.com> wrote:
> On Sunday, December 12, 2021 at 1:22:35 PM UTC-8, konyberg wrote:
>> søndag 12. desember 2021 kl. 21:45:07 UTC+1 skrev mitchr...@gmail..com:
>> > 1/3*3=1
>> > but .333 does not equal 1/3
>> > Those are different in quantity
>> > and representation.
>> > Calculus shows the difference
>> > by what builds sizes of infinity
>> > instead.

>> > Mitchell Raemsch
>> .333 is not equal to 1/3. That is true! But 0.333... is equal to 1/3.
>> KON

> You can't have it both ways. They are both different...

Not at all. Only one of them's different. The other one's the same.

> in either order...

--
Alan Mackenzie (Nuremberg, Germany).

On Monday, December 13, 2021 at 3:13:13 AM UTC-8, Alan Mackenzie wrote:
> mitchr...@gmail.com <mitchr...@gmail.com> wrote:
> > On Sunday, December 12, 2021 at 1:22:35 PM UTC-8, konyberg wrote:
> >> søndag 12. desember 2021 kl. 21:45:07 UTC+1 skrev mitchr...@gmail..com:
> >> > 1/3*3=1
> >> > but .333 does not equal 1/3
> >> > Those are different in quantity
> >> > and representation.
> >> > Calculus shows the difference
> >> > by what builds sizes of infinity
> >> > instead.
>
> >> > Mitchell Raemsch
> >> .333 is not equal to 1/3. That is true! But 0.333... is equal to 1/3.
> >> KON
>
> > You can't have it both ways. They are both different...
> Not at all. Only one of them's different. The other one's the same.

Alan? You need two to have a difference...

Mitchell Raemsch
>
> > in either order...
>
> --
> Alan Mackenzie (Nuremberg, Germany).

mandag 13. desember 2021 kl. 18:27:52 UTC+1 skrev mitchr...@gmail.com:
> On Monday, December 13, 2021 at 3:13:13 AM UTC-8, Alan Mackenzie wrote:
> > mitchr...@gmail.com <mitchr...@gmail.com> wrote:
> > > On Sunday, December 12, 2021 at 1:22:35 PM UTC-8, konyberg wrote:
> > >> søndag 12. desember 2021 kl. 21:45:07 UTC+1 skrev mitchr...@gmail.com:
> > >> > 1/3*3=1
> > >> > but .333 does not equal 1/3
> > >> > Those are different in quantity
> > >> > and representation.
> > >> > Calculus shows the difference
> > >> > by what builds sizes of infinity
> > >> > instead.
> >
> > >> > Mitchell Raemsch
> > >> .333 is not equal to 1/3. That is true! But 0.333... is equal to 1/3..
> > >> KON
> >
> > > You can't have it both ways. They are both different...
> > Not at all. Only one of them's different. The other one's the same.
> Alan? You need two to have a difference...
>
> Mitchell Raemsch
> >
> > > in either order...
> >
> > --
> > Alan Mackenzie (Nuremberg, Germany).

Mitch. Why don't you try to devide 1 by 3. I think that you'll find 1/3 = 0.333...
If not give us where the desimal differs from 3. And don't come back before finished!
KON

On Monday, December 13, 2021 at 11:55:19 AM UTC-8, konyberg wrote:
> mandag 13. desember 2021 kl. 18:27:52 UTC+1 skrev mitchr...@gmail.com:
> > On Monday, December 13, 2021 at 3:13:13 AM UTC-8, Alan Mackenzie wrote:
> > > mitchr...@gmail.com <mitchr...@gmail.com> wrote:
> > > > On Sunday, December 12, 2021 at 1:22:35 PM UTC-8, konyberg wrote:
> > > >> søndag 12. desember 2021 kl. 21:45:07 UTC+1 skrev mitchr...@gmail.com:
> > > >> > 1/3*3=1
> > > >> > but .333 does not equal 1/3
> > > >> > Those are different in quantity
> > > >> > and representation.
> > > >> > Calculus shows the difference
> > > >> > by what builds sizes of infinity
> > > >> > instead.
> > >
> > > >> > Mitchell Raemsch
> > > >> .333 is not equal to 1/3. That is true! But 0.333... is equal to 1/3.
> > > >> KON
> > >
> > > > You can't have it both ways. They are both different...
> > > Not at all. Only one of them's different. The other one's the same.
> > Alan? You need two to have a difference...
> >
> > Mitchell Raemsch
> > >
> > > > in either order...
> > >
> > > --
> > > Alan Mackenzie (Nuremberg, Germany).
> Mitch. Why don't you try to devide 1 by 3. I think that you'll find 1/3 = 0.333...

It does not go all of the way, Instead of a zero difference
substitute an unlimited small...

Mitchell Raemsch

On 12/12/2021 12:45 PM, mitchr...@gmail.com wrote:
> 1/3*3=1
> but .333 does not equal 1/3
> Those are different in quantity
> and representation.
> Calculus shows the difference
> by what builds sizes of infinity
> instead.

1/3*3=1

1/3=.333... in base ten

..333... * 3 = 1 in base ten.

Get over it!

..3333... is represented as 1/3 in base ten trying to approximate it as
closely as possible in the given base, get over it! .333... * 3 = 1, as
1/3*3=1.

Got it?

Then we can go step-by-step and never reach 1, but that is a different
and fun way to approach the limit, so to speak...

On Sunday, December 12, 2021 at 3:45:07 PM UTC-5, mitchr...@gmail.com wrote:
> 1/3*3=1
> but .333 does not equal 1/3
> Those are different in quantity
> and representation.
> Calculus shows the difference
> by what builds sizes of infinity
> instead.
>
> Mitchell Raemsch

We really should enter the interpretation that
1/3 = 0 remainder 1
into this discussion at some point.
As the remainder is as its name implies then the statement:
1/3 = 0
holds true. These numbers are natural values within this interpretation.
Yes, I should have said that up front.
Call it tricky, yet in discrete systems this is the case.
Discrete in, discrete out.
Who breaks the mold?
Into the continuum?
As our president is fond of saying:
" C'moon, Maaan."
And now for the push-up contest.

On 12/14/2021 9:39 AM, Timothy Golden wrote:
> On Sunday, December 12, 2021 at 3:45:07 PM UTC-5, mitchr...@gmail.com wrote:
>> 1/3*3=1
>> but .333 does not equal 1/3
>> Those are different in quantity
>> and representation.
>> Calculus shows the difference
>> by what builds sizes of infinity
>> instead.
>>
>> Mitchell Raemsch
>
> We really should enter the interpretation that
> 1/3 = 0 remainder 1

nope, 1/3 base(1/3) = 1 with a remainder of 0

> As our president is fond of saying:
> " C'moon, Maaan."

he doesn't know he is saying that, he thinks he is farting.

> And now for the push-up contest.

On Tuesday, December 14, 2021 at 8:29:09 AM UTC-8, Serg io wrote:
> On 12/14/2021 9:39 AM, Timothy Golden wrote:
> > On Sunday, December 12, 2021 at 3:45:07 PM UTC-5, mitchr...@gmail.com wrote:
> >> 1/3*3=1
> >> but .333 does not equal 1/3
> >> Those are different in quantity
> >> and representation.
> >> Calculus shows the difference
> >> by what builds sizes of infinity
> >> instead.
> >>
> >> Mitchell Raemsch
> >

The unlimited small and zero behave the same.

mitchr...@gmail.com <mitchrae3323@gmail.com> wrote:
> On Tuesday, December 14, 2021 at 8:29:09 AM UTC-8, Serg io wrote:
>> On 12/14/2021 9:39 AM, Timothy Golden wrote:
>> > On Sunday, December 12, 2021 at 3:45:07 PM UTC-5,
>> > mitchr...@gmail.com wrote:
>> >> 1/3*3=1 but .333 does not equal 1/3 Those are different in quantity
>> >> and representation. Calculus shows the difference by what builds
>> >> sizes of infinity instead.

>> >> Mitchell Raemsch

> The unlimited small and zero behave the same.

Indeed, that is what we are watching.

--
Alan Mackenzie (Nuremberg, Germany).

On Tuesday, December 14, 2021 at 2:10:54 PM UTC-8, Alan Mackenzie wrote:
> mitchr...@gmail.com <mitchr...@gmail.com> wrote:
> > On Tuesday, December 14, 2021 at 8:29:09 AM UTC-8, Serg io wrote:
> >> On 12/14/2021 9:39 AM, Timothy Golden wrote:
> >> > On Sunday, December 12, 2021 at 3:45:07 PM UTC-5,
> >> > mitchr...@gmail.com wrote:
> >> >> 1/3*3=1 but .333 does not equal 1/3 Those are different in quantity
> >> >> and representation. Calculus shows the difference by what builds
> >> >> sizes of infinity instead.
>
> >> >> Mitchell Raemsch
>
>
> > The unlimited small and zero behave the same.
> Indeed, that is what we are watching.
> --
> Alan Mackenzie (Nuremberg, Germany).

They are both dark as no quantity and first following it...

onsdag 15 december 2021 kl. 19:53:33 UTC+1 skrev mitchr...@gmail.com:
> On Tuesday, December 14, 2021 at 2:10:54 PM UTC-8, Alan Mackenzie wrote:
> > mitchr...@gmail.com <mitchr...@gmail.com> wrote:
> > > On Tuesday, December 14, 2021 at 8:29:09 AM UTC-8, Serg io wrote:
> > >> On 12/14/2021 9:39 AM, Timothy Golden wrote:
> > >> > On Sunday, December 12, 2021 at 3:45:07 PM UTC-5,
> > >> > mitchr...@gmail.com wrote:
> > >> >> 1/3*3=1 but .333 does not equal 1/3 Those are different in quantity
> > >> >> and representation. Calculus shows the difference by what builds
> > >> >> sizes of infinity instead.
> >
> > >> >> Mitchell Raemsch
> >
> >
> > > The unlimited small and zero behave the same.
> > Indeed, that is what we are watching.
> > --
> > Alan Mackenzie (Nuremberg, Germany).
> They are both dark as no quantity and first following it...
blah blah blah you do not understand mathematics

On Tuesday, December 14, 2021 at 11:29:09 AM UTC-5, Serg io wrote:
> On 12/14/2021 9:39 AM, Timothy Golden wrote:
> > On Sunday, December 12, 2021 at 3:45:07 PM UTC-5, mitchr...@gmail.com wrote:
> >> 1/3*3=1
> >> but .333 does not equal 1/3
> >> Those are different in quantity
> >> and representation.
> >> Calculus shows the difference
> >> by what builds sizes of infinity
> >> instead.
> >>
> >> Mitchell Raemsch
> >
> > We really should enter the interpretation that
> > 1/3 = 0 remainder 1
> nope, 1/3 base(1/3) = 1 with a remainder of 0

Hmmm.... haven't gone there yet.
Bravo for covering some new ground, Sergio.

As I see it the discussion on closure could have been engaged at this juncture.
It should be said that the rational value makes a break with closure.
Within operator theory it is a sore thumb.
It does not help that division is a non-commutative operation.
With this as the basis on which the mathematicians' continuum rests
I might be able to win the push-up contest.

So who has the more pure value? Who is it that builds the continuum?
It is of course the one who can vary unity.
It is the one which has slightly more structure than the natural value.
Yet it is that one which still carries a natural valued interpretation as well.
As far as I am concerned
0.333
will do just fine but for 0.001
and if you'd like we can do better.

This is all that epsilon/delta promises and it is all that is needed to settle the dispute.
That a 'rational' value can be treated as on equal footing with the others...
This is done via the decimal point. This is done with attention to precision.
This is done daily by engineers and physicists
while the mathematicians sit at the side lines naying.

It would be of great utility to enter into the conversation the issue of the theoretical versus the experimental.
As such we know that theory is to be a pristine thing.
Here obviously the mathematician is the one who has gone astray.

He claims closure down the road yet denies it when it does not suit his needs.
He happily builds in exceptions to his rules when his rules don't quite work.
And so the mathematician's own attachment to detachment to experimental works lands him
in a heap that has grown so large in useless terminology and branchings
the shards of which litter wikipedia and competing mathematics sites
as the PhDs branch ever further into the vacuum for need of space to grow
their noninstantiable forms and meanders
that we might as well be mice squeaking against an avalanche,
But Squeak We Must!
> > As our president is fond of saying:
> > " C'moon, Maaan."
> he doesn't know he is saying that, he thinks he is farting.
> > And now for the push-up contest.

On 12/16/2021 8:02 AM, Timothy Golden wrote:
> On Tuesday, December 14, 2021 at 11:29:09 AM UTC-5, Serg io wrote:
>> On 12/14/2021 9:39 AM, Timothy Golden wrote:
>>> On Sunday, December 12, 2021 at 3:45:07 PM UTC-5, mitchr...@gmail.com wrote:
>>>> 1/3*3=1
>>>> but .333 does not equal 1/3
>>>> Those are different in quantity
>>>> and representation.
>>>> Calculus shows the difference
>>>> by what builds sizes of infinity
>>>> instead.
>>>>
>>>> Mitchell Raemsch
>>>
>>> We really should enter the interpretation that
>>> 1/3 = 0 remainder 1
>> nope, 1/3 base(1/3) = 1 with a remainder of 0
>
> Hmmm.... haven't gone there yet.
> Bravo for covering some new ground, Sergio.
>
> As I see it the discussion on closure could have been engaged at this juncture.
> It should be said that the rational value makes a break with closure.
> Within operator theory it is a sore thumb.
> It does not help that division is a non-commutative operation.
> With this as the basis on which the mathematicians' continuum rests
> I might be able to win the push-up contest.
>
> So who has the more pure value? Who is it that builds the continuum?

the continuum is already built, the continuum continues...

> It is of course the one who can vary unity.
> It is the one which has slightly more structure than the natural value.
> Yet it is that one which still carries a natural valued interpretation as well.
> As far as I am concerned
> 0.333

0.333 is 666/2000 sign of the devil or 1/2000 of the devil.

> will do just fine but for 0.001
> and if you'd like we can do better.
>
> This is all that epsilon/delta promises and it is all that is needed to settle the dispute.
> That a 'rational' value can be treated as on equal footing with the others...
> This is done via the decimal point. This is done with attention to precision.
> This is done daily by engineers and physicists
> while the mathematicians sit at the side lines naying.
>
> It would be of great utility to enter into the conversation the issue of the theoretical versus the experimental.
> As such we know that theory is to be a pristine thing.
> Here obviously the mathematician is the one who has gone astray.
>
> He claims closure down the road yet denies it when it does not suit his needs.
> He happily builds in exceptions to his rules when his rules don't quite work.
> And so the mathematician's own attachment to detachment to experimental works lands him
> in a heap that has grown so large in useless terminology and branchings
> the shards of which litter wikipedia and competing mathematics sites
> as the PhDs branch ever further into the vacuum for need of space to grow
> their noninstantiable forms and meanders
> that we might as well be mice squeaking against an avalanche,
> But Squeak We Must!

so, you are pro-mousie ?

>
>>> As our president is fond of saying:
>>> " C'moon, Maaan."
>> he doesn't know he is saying that, he thinks he is farting.
>>> And now for the push-up contest.
>

On Wednesday, December 15, 2021 at 9:21:56 PM UTC-8, zelos...@gmail.com wrote:
> onsdag 15 december 2021 kl. 19:53:33 UTC+1 skrev mitchr...@gmail.com:
> > On Tuesday, December 14, 2021 at 2:10:54 PM UTC-8, Alan Mackenzie wrote:
> > > mitchr...@gmail.com <mitchr...@gmail.com> wrote:
> > > > On Tuesday, December 14, 2021 at 8:29:09 AM UTC-8, Serg io wrote:
> > > >> On 12/14/2021 9:39 AM, Timothy Golden wrote:
> > > >> > On Sunday, December 12, 2021 at 3:45:07 PM UTC-5,
> > > >> > mitchr...@gmail.com wrote:
> > > >> >> 1/3*3=1 but .333 does not equal 1/3 Those are different in quantity
> > > >> >> and representation. Calculus shows the difference by what builds
> > > >> >> sizes of infinity instead.
> > >
> > > >> >> Mitchell Raemsch
> > >
> > >
> > > > The unlimited small and zero behave the same.
> > > Indeed, that is what we are watching.
> > > --
> > > Alan Mackenzie (Nuremberg, Germany).
> > They are both dark as no quantity and first following it...
> blah blah blah you do not understand mathematics

Differences plotted on the quantity line are real
just as difference in representation is...
..9 repeating and first integer have their difference.

Mitchell Raemsch

torsdag 16 december 2021 kl. 20:00:46 UTC+1 skrev mitchr...@gmail.com:
> On Wednesday, December 15, 2021 at 9:21:56 PM UTC-8, zelos...@gmail.com wrote:
> > onsdag 15 december 2021 kl. 19:53:33 UTC+1 skrev mitchr...@gmail.com:
> > > On Tuesday, December 14, 2021 at 2:10:54 PM UTC-8, Alan Mackenzie wrote:
> > > > mitchr...@gmail.com <mitchr...@gmail.com> wrote:
> > > > > On Tuesday, December 14, 2021 at 8:29:09 AM UTC-8, Serg io wrote:
> > > > >> On 12/14/2021 9:39 AM, Timothy Golden wrote:
> > > > >> > On Sunday, December 12, 2021 at 3:45:07 PM UTC-5,
> > > > >> > mitchr...@gmail.com wrote:
> > > > >> >> 1/3*3=1 but .333 does not equal 1/3 Those are different in quantity
> > > > >> >> and representation. Calculus shows the difference by what builds
> > > > >> >> sizes of infinity instead.
> > > >
> > > > >> >> Mitchell Raemsch
> > > >
> > > >
> > > > > The unlimited small and zero behave the same.
> > > > Indeed, that is what we are watching.
> > > > --
> > > > Alan Mackenzie (Nuremberg, Germany).
> > > They are both dark as no quantity and first following it...
> > blah blah blah you do not understand mathematics
> Differences plotted on the quantity line are real
> just as difference in representation is...
> .9 repeating and first integer have their difference.
>
> Mitchell Raemsch
There is no difference, they are exactly equal

On 12/16/2021 2:00 PM, mitchr...@gmail.com wrote:
> Differences plotted on the quantity line are real
> just as difference in representation is...
> .9 repeating and first integer have their difference.

Yes, Roy, that difference is 0.

On Thursday, December 16, 2021 at 9:16:23 PM UTC-8, zelos...@gmail.com wrote:
> torsdag 16 december 2021 kl. 20:00:46 UTC+1 skrev mitchr...@gmail.com:
> > On Wednesday, December 15, 2021 at 9:21:56 PM UTC-8, zelos...@gmail.com wrote:
> > > onsdag 15 december 2021 kl. 19:53:33 UTC+1 skrev mitchr...@gmail.com:
> > > > On Tuesday, December 14, 2021 at 2:10:54 PM UTC-8, Alan Mackenzie wrote:
> > > > > mitchr...@gmail.com <mitchr...@gmail.com> wrote:
> > > > > > On Tuesday, December 14, 2021 at 8:29:09 AM UTC-8, Serg io wrote:
> > > > > >> On 12/14/2021 9:39 AM, Timothy Golden wrote:
> > > > > >> > On Sunday, December 12, 2021 at 3:45:07 PM UTC-5,
> > > > > >> > mitchr...@gmail.com wrote:
> > > > > >> >> 1/3*3=1 but .333 does not equal 1/3 Those are different in quantity
> > > > > >> >> and representation. Calculus shows the difference by what builds
> > > > > >> >> sizes of infinity instead.
> > > > >
> > > > > >> >> Mitchell Raemsch
> > > > >
> > > > >
> > > > > > The unlimited small and zero behave the same.
> > > > > Indeed, that is what we are watching.
> > > > > --
> > > > > Alan Mackenzie (Nuremberg, Germany).
> > > > They are both dark as no quantity and first following it...
> > > blah blah blah you do not understand mathematics
> > Differences plotted on the quantity line are real
> > just as difference in representation is...
> > .9 repeating and first integer have their difference.
> >
> > Mitchell Raemsch
> There is no difference, they are exactly equal

No. They are different by the closest thing to zero
on the number line...

Mitchell Raemsch

On Thursday, December 16, 2021 at 10:51:48 AM UTC-5, Serg io wrote:
> On 12/16/2021 8:02 AM, Timothy Golden wrote:
> > On Tuesday, December 14, 2021 at 11:29:09 AM UTC-5, Serg io wrote:
> >> On 12/14/2021 9:39 AM, Timothy Golden wrote:
> >>> On Sunday, December 12, 2021 at 3:45:07 PM UTC-5, mitchr...@gmail.com wrote:
> >>>> 1/3*3=1
> >>>> but .333 does not equal 1/3
> >>>> Those are different in quantity
> >>>> and representation.
> >>>> Calculus shows the difference
> >>>> by what builds sizes of infinity
> >>>> instead.
> >>>>
> >>>> Mitchell Raemsch
> >>>
> >>> We really should enter the interpretation that
> >>> 1/3 = 0 remainder 1
> >> nope, 1/3 base(1/3) = 1 with a remainder of 0
> >
> > Hmmm.... haven't gone there yet.
> > Bravo for covering some new ground, Sergio.
> >
> > As I see it the discussion on closure could have been engaged at this juncture.
> > It should be said that the rational value makes a break with closure.
> > Within operator theory it is a sore thumb.
> > It does not help that division is a non-commutative operation.
> > With this as the basis on which the mathematicians' continuum rests
> > I might be able to win the push-up contest.
> >
> > So who has the more pure value? Who is it that builds the continuum?
> the continuum is already built, the continuum continues...
> > It is of course the one who can vary unity.
> > It is the one which has slightly more structure than the natural value.
> > Yet it is that one which still carries a natural valued interpretation as well.
> > As far as I am concerned
> > 0.333
> 0.333 is 666/2000 sign of the devil or 1/2000 of the devil.
> > will do just fine but for 0.001
> > and if you'd like we can do better.
> >
> > This is all that epsilon/delta promises and it is all that is needed to settle the dispute.
> > That a 'rational' value can be treated as on equal footing with the others...
> > This is done via the decimal point. This is done with attention to precision.
> > This is done daily by engineers and physicists
> > while the mathematicians sit at the side lines naying.
> >
> > It would be of great utility to enter into the conversation the issue of the theoretical versus the experimental.
> > As such we know that theory is to be a pristine thing.
> > Here obviously the mathematician is the one who has gone astray.
> >
> > He claims closure down the road yet denies it when it does not suit his needs.
> > He happily builds in exceptions to his rules when his rules don't quite work.
> > And so the mathematician's own attachment to detachment to experimental works lands him
> > in a heap that has grown so large in useless terminology and branchings
> > the shards of which litter wikipedia and competing mathematics sites
> > as the PhDs branch ever further into the vacuum for need of space to grow
> > their noninstantiable forms and meanders
> > that we might as well be mice squeaking against an avalanche,
> > But Squeak We Must!
> so, you are pro-mousie ?

Well I do like mousy women.
Maybe it's from childhood with those mouse families living mouse lives with good mouse mothers.
All very cute and cuddly, well dressed and equipped with metal rimmed spectacles when needed.
Of course these days I do set traps for them and they go into the compost.
I've thought maybe if I neutered some territorial males some sort of a a truce could be had.
I'm afraid though that project is on hold.
We are caught here guarding our supplies against the meekest of foes.
The human condition and its escapement is a worthy pursuit of the mathematician,
yet when he lands himself in a sticky quagmire and loses his boots in the goop of the swamp after breaking through the rotten floorboards of his bridge then what?

This is roughly the position I am in, though not far away lay some stepping stones.
Barefoot there is nothing left to loose.
At least in that way we can go forward unencumbered.
Of course I'd like to land with a new pair of shoes.
Possibly skis built in.
Just enough to float the swamp.

The repeating decimal form shows up regularly and is challenged regularly.
The usage of ellipses within mathematics is an implementation of infinity.
Whether that is valid is at some level a personal choice.
Interpretation plays a part in this.
Digital analysis is beneath most mathematicians.
Yet since ambiguities do lay there it puts them on false footings.

It is not as if I have resolved this completely, but I do see through the menagerie that the real analysis composes from.
So shall we get on to a new term for 'reality'?
Yet then should we name our new numbers by this would we be setting up for the next cultural divide?
The sheer quantity of subdivisions ought to be puzzling to the mathematical mind.
Simplicity was to be the focus of mathematics.
Academia has another thing in mind.
There was a time when this thing worked differently.
I recommend adoption of that earlier mindset.
It's not as if I can digest all of every branch or even one branch completely in the accumulated pile.
It is too easy to shirk the whole business and call it all crap.
I wouldn't be here if that were the case.
Still something is amiss and I'm fairly sure that we are not so far beyond the mice.
That we are merely in the midst of a progression is a substantial realization.
This is why the stepping stones matter.
To form the next bridge we must cover the ground and know it well.
Well enough to get some better footings than the last bridge.
Of course it is an individual pursuit.
There is room for all to be bridging their own way.
So we are like mice again.
Squeak We Must.

To what degree are our numbers merely a means of brevity?
To what degree is the means of brevity in the way of pure analysis?
I'm pretty sure this is where the 'naturals' among us go as I bog down in modulo thinking.
Yet some options within the modulo thinking have been overlooked by those naturalists.
They divorce themselves from sign.
Their own usage of inversion must be disputed.
Meanwhile my own goes understated yet its existence is trivial.
It then wraps around onto operator theory
rotating kaleidoscopically in general dimension
dismantling much of standing mathematical theory.

> >
> >>> As our president is fond of saying:
> >>> " C'moon, Maaan."
> >> he doesn't know he is saying that, he thinks he is farting.
> >>> And now for the push-up contest.
> >