Huzzah, Burns: "Bizarre-o-Meter".
Or, excuse me, "Bizarre-O-Meter(tm)".
The: "... if you tried to
take their infinities away,
their _continuous media_, ...",
the implied tension and the
fanaticism for "the continuous media",
I forward your opinion.
Infinity, though, Jerry, I don't really
think "Do we really need the concept of
infinity" as much as "does the concept
of infinity really need us".
Here that's where there is infinity,
then there basically is whether there
is or not.
It's pretty well established in the
classical laws the continuum mechanics
are pretty well established reasonable
expectation of usually "continuous"
terms and how in the arithmetic the
expression (as of cases of induction)
the discrete is in terms of infinitely-
many terms. It's just not so for where
it's not.
That's of course besides that there's
all the solutions in the middle, here
all finite terms and finite combinatorics
and results in finite groups and usually
the all sorts of finite algebras as altogether
build for usual families all sorts of expressions
finite and infinite, and here for numerical methods
and of terms.
There's certainly "all" the finite, that's no
different than "infinite" to me.
"Than" or "from", "no different from infinite"
or "no difference from infinite".
Then "than" or "from" is an ad-hoc convention
for example for expressions for different and
difference in the value for example, with
approximations as not different (in terms,
always if not eventually with errors, for
for the functional and replete besides the
pragmatic).
That's an example, a convention or accommodation
for "infinitely-many" any why or why not in terms,
while in a first-order system, measurement or
along those lines is built in finite terms,
classical constructions and as above.
It's not that I care about "infinity",
it's certainly all that it is whether I care.
Makes sense to me for anybody else to feel the same way.
Then, the mathematics and finite and discrete
mathematics as a discipline (among for example
the world of established results in continuous
functions, here often and in the canon expressions
as above), as a discipline, quite certainly isn't
lacking in quite most usual applications, for
that there is yet the "extra".
Plainly it's the continuous has infinitely-many
discrete terms or what would be parts or here
some continuous "media" (or usually, "region")
in the terms, it would be a contradiction for
it not to (have infinitely-many parts), the
continuous media. Here "infinitely many parts"
is "each the same" or "the same size". (Clearly
continuous media can be put to finitely many
parts of various sizes, for example a line
on a plane.)
"Finitism" is completely reasonable (finitism
with infinite integers, or any some of them
in order that go on past ever their count).
"Retro-finitism" or figuring to negate
is for crankety trolls. Retro-finitism
is for crankety trolls and they can get bent.
"Finitism" is perfectly reasonable: in terms.
As a concept, though, "Infinity" it seems rather
the point of the integers to have that there.