From Newsgroup: sci.math

On 06/12/2024 12:30 PM, Ross Finlayson wrote:

On 06/12/2024 09:49 AM, FromTheRafters wrote:

Ross Finlayson formulated the question :

On 06/11/2024 04:17 PM, Moebius wrote:

Am 12.06.2024 um 01:13 schrieb Ross Finlayson:

There's a difference between "any precision" and "no difference".

Indeed!

In other words, "any precision" and "no difference" is not the same.
:-)

Or, "calculus is only real in the infinite, not merely the finite".

The reals are pretty much defined by calculus aren't they?

Hardy equates them with magnitudes of points on a line
given a unit magnitude, then with differences for the
unsigned magnitudes and signed quantities.

The reals are "continuous", they're nowhere "discontinuous",
and yes I know that's into matters of definition.

The reals represent the modular, the ordinary, the scalar,
and particularly the scalar, and the continuous, as far
as that the reals are the numbers modeled by a "Linear
Continuum", and scalar values.

Calculus is pretty much defined by infinitesimals,
i.e., infinite sums in the infinite limit when
differences go to zero, and mostly formally about
these in ratio.

Calculus is defined by the fundamental theorems of
the derivative and integral, which follows from
the laws of arithmetic because the real numbers
are trichotomous, and the intermediate value theorem.

Then, there are also notions of the _singular integrals_
with their singularities and thus multiplicities and
branch points and branches of analysis, and derivatives
have their asymptotes for example, or anything to do
with hysteresis. Also the calculus is considered as
with regards to the continuous and discontinuous,
cadlag and so on, for example as after Poincare,
and, Dirichlet.

Calculus is usually ascribed to Leibniz and Newton,
and the notation is the notation of Leibniz, and
Maclaurin wrote the formalism, and these days the
formalism is often given to Cauchy and Weierstrass
for the infinite limit, the Riemann and Lebesgue,
then about Stieltjes and Jordan, then also as with
regards to Feynman and London, the meromorphic and
symplectic.

The calculus of integral equations and calculus of
differential equations and the differ-integro and
integro-differ are, kind of different each other.

So, most equate them with points on the real number line.

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