Post by SergioPost by Ross A. FinlaysonPost by SergioPost by Ross A. FinlaysonPost by FromTheRaftersPost by WMPost by FromTheRaftersPost by Fritz FeldhasePost by FromTheRaftersProof (by induction): E(1) = IN, hence E(1) is infinite. [...]
E(1) does not equal the naturals in muckymath.
*sigh*
Hint: "With E(1) = ℕ all is said. But that should be known meanwhile." (WM,
sci.math)
Hope this helps.
It doesn't. The index for the endsegment should be the same as the
greatest element of the associated FISON *plus* one.
That would be possible, perhaps even better. But I have originally defined it
in this way: F(n) = {1, 2, 3, ..., n}
E(n) = {n, n+1, n+2, ...}
E(n) then intersects F(n) at n when they are supposed to be the
disjoint (complementary) subsets of the newly partitioned naturals. But
okay, muckymath is bulletproof with the axiom of because I (WM) said
so.
Carry on.
Think of it this way: "it had carried on then for whatever reason,
the condition changed: it's the same axiomatic system, including a dynamic".
That simply changes what is the parallel condition in the finite,
to be just the same way, axiomatic in dynamics.
Then, all your moot arguments are compressible to a pinhead.
The axiomatic and dynamic, is much simpler and better,
than argument, in terms of unending argument and regress.
Though it involves reasoning facilities, axiomatics is dynamic
in the sense of the very strong axiomatic, what must entail
all reasoning facilities: at least this simple axiomatic is simply
dynamic: whatever all faults in reasoning reduce to induction.
The utterly and fundamentally technical, here for the infinite
there's that WM's failed induction over a related rates system,
because his relation that is proportional is first not second
that there is an infinite rate, (respectively not a largest finite rate).
Then, having the proportional that runs out together is a related
rate, any matter of proportion in time.
This assumes a linear constant rate of time at least from every
object in space-time, or the local rate down to zero.
Which leaves though both sides having brought down the
others' reasoning, while still having to leave them together.
Then, this leads immediately to my slates and the state of
modern axiomatics in continuum analysis, neatly out.
"It's easy to be a troll when mathematics does all the work of being right."
"Shannon is sometimes given credit for Nyquist theorem,
where it may be so that Shannon and "continuity is result
of rationals" have that Shannon's results in signal theory
and for information theory, for information theory, and,
signal theory, with respect to formalism and here with
formalism in foundations, have that "no, it is not so that
'continuity is result of rationals', it's not to be implied
that it's a point of Shannon's when connecting signal theory
and properties of continuous sampling theorems, except
to illustrate the entire connection here in the abstract."
agree, its abstraction.
Then, that "I said so", is basically that mostly I have
studied the formalism of the line continuity and the
field continuity, with respect to the signal continuity,
and continuous functions which is the usual formalism. "
line integrals too ?
Sure, mathematics does all the work of being right.
Line integrals are difficult also rudimentary.
Solving all WM's problems in related rates,
and with assigning the limits as opaque,
results why what falls out.
The line integral, introduced after the area integral,
and for surface integrals in a similar sense, and
the path of integration, is that there is the path integral.
Then, it is also some "bridge integral". I.e., the path
is defined according to its bounds, what for example, is
the "path integral, add up where it's been", for the
bridge integral, partition where it's going".
The line integral is often contrived "end-of-the-line" interal,
i.e., "a line integral is always attached". But, of course
it's still the exact same interpretation, "the length of the line".
Now, I just introduced or "defined", bridge integral, though
it's usually just the shortest line integral, that also happens
for attachments across the square or the angle, what's drawn out.
(Square, radial, anti-logarithmic, ....)
That the differential is anti-integral is vice-versa.
The antilogarithm or power, is for tables: under linear inputs, usually.
Paint cans are volume but usually define what area they cover.
Why are you bringing line integral into it? Isn't that contrived
for either the catenary or parabolic?
google line integrals,
Just testing to see how much math you know, like a sounding, this one is by the Deep One less four quarters.
"That was the greatest comic tour de force that anybody had seen in a long time."
(Roger Rabbit)
The line integral was introduced after the catenary problem,
basically at the end of otherwise a chapter in the text, instead
of starting a new chaper, the "advanced calculus". So, I wanted
to make the line integral the same as the quarter-bend, but instead
it was both amounting to the catenary via parabola, and, that
I want to solve the catenary in the parabola, but, otherwise the
line integral was let down to line elements and ds.
Then the surface integral, after surfaces of revolution, or paint cans,
then the path of integration is free for what it is, what it amounts to.
So, I'd imagine several line integral setups for usual problems of
what is the length according to perimeter, circumference, besides
as wise the square, and quadratic, in the elements, and the paths.
This is where according to the paths there are elements that are
integrable, that any contrivance in symmetry or exhaust, or relation
in measure here length, is for usual geometric and stateful examples,
in terms of how and why they are line elements and path elements.
The "advanced calculus", ..., here when it got to "yes I have derived this
Green's function accordingly, but, what I want is instead for example
different elements", then though later after gradient descent and
Stokes, then again out through the Hamiltonian what really though
is for the Hermitian, then to flow and what is fluid mechanics and
fluid dynamics, then again it was "still these are Green's functions
after Stokes, 'advanced calculus'", I've studied the advanced calculus,
and have several texts, but surely most my exposure is peripheral.
I.e. the brief tableau for the determinantal, the "dot product is ...
derivative anti-integral placeholder-element", is for people to
learn inner and outer products and wedge and dot and so on.
And why and how it's computable.
Read this "Exterior derivative" Wiki: https://en.wikipedia.org/wiki/Exterior_derivative
Then you'll notice it's as if I intend to paste the above into it.