What does 1 have to do with 2?
- From: "M.M.M." <marty.musatov@xxxxxxxxx>
- Date: Thu, 20 Aug 2009 19:06:43 -0700 (PDT)
Invaluable! Thank you. (My responses are mixed in with yours)
MM: What if we said (we simply read):
RG: Do you think that the limit definition of the derivative, and
Reimann
Sums do not illustrate derivatives and integrals in a useful way?
MM: I think the Riemann Sums and the limit definition of the
derivative are exceptionally illustrative of derivatives and integrals
in a very userful way and that they may be looked at like stepping
stones to discoveries we might have missed without them!
RG: I'm not sure I understand this demonstration (below)... it seems
to be
getting at the idea of approaching, always getting closer, but never
reaching a point. But it totally eludes the slope of a secant --
which
gives an average rate of change ... and the slope of a tangent --
which
gives an instantaneous rate of change. These are the useful concepts
in
calculus...
MM: While I indeed agree these things (the slope of a secant and the
useful properties it contains and the slope of a tangent as an
instantaneous rate of change) are (indeed) useful and no doubt my
ommission is (in fact) a glaring confession of my total ignorance of
how exactly these things relate to language and practical
applications, I am searching for a more flexible form that might be
more appropriate for lazy smart people like me who want to overturn
the foundations of mathematics with a Screenwriting degree and only a
single Liberal Arts Math class at the college level. What I am getting
at however labouriously is if we can tell they elude a point does this
preclude the point we may derive anything useful from them if they
observe a consistent form? I love language and how it relates to
mathematics. So if you will excuse my lyrical indulgence (perhaps even
if only out of kindness to a cousin) does it matter to me (does it
matter in math) the motive which a variable acquiesces a solutive? (I
am sincerely greatful and I hope obviously only conceding this
possibility to make a point.)
The point is to look at the definition limit of 'elude':(s)
Inflected Form(s): elud·ed; elud·ing• Etymology: Latin
eludere, from e- + ludere to play — more at ludicrous• Date: 1667 1 :
to avoid adroitly : evade <the mice eluded the traps> <managed to
elude capture> 2 : to escape the perception, understanding, or grasp
of <subtlety simply eludes them> <victory continued to elude us> 3 :
defy 4 <it eludes explanation>synonyms see escape(L)anguange: this
last bit is mine kind of sort of...
Like when youthen it has a derivative at any point on that interval (but I'm
walk
down
steps
sideways
one
foot
at
a
time
and
you
will find
you
step
back
each
time
you
take
a
step;
you
always
step
back
and
it
never
ends.
This is the (idea) and here is how I (applied) it to P Versus NP:
My
name
is
Martin
M
ichael
Mu
satov
Mus
atov
Reso
loved
P
Versus
NP
this
way
did
he
prove
that
P
=
NP
Q.
E.
D
.
And
this
was/is
how
I
proved
that
beyond:
P = NP
is beyond
doubt
reasonable
to
prove
P = / = NP
is
beyond reason. P = NP. Q.E.D. Musatov
To
P
Vs.
NP
is
you
will
find
y
ou really
ste
p back
each
time
you
take
a
step;
Can
Play
In
Poly
nomial
time
this
way
Here is my question:
Preface:
I have read the following four (perhaps incomplete) statements based
on the Fundamental Theorem of Calculus:
1. If f is continuous on the interval [a,b] then FTC...
thinking
it should be an open interval (a,b) not closed [a,b])
RG: What are a(x) and b(x)? functions? different from f(x)?
2. if F(x) is a function for which f(x) is the derivative, then the
integral of f(x) on the interval [a,b] is equal to F(b) - F(a).
3. The area under the graph of a function over an interval can be
calculated by evaluating any antiderivative.
4. (The “Generalized” First Fundamental Theorem of Calculus) Let f be
con - tinuous on (−∞,∞) and let a(x),b(x) be differentiable on (−∞,∞).
MM: (Father, please forgive me if I insult this woman by reaching out
of willfull ignorance)
A function, written with a syntax like f:=x->x^2+5*x+6, is different
from the (...) result (as an arrow-defined function), you have to
f:=unapply(a*x+b,x)
(Which I am wondering why wouldn't that take us into this space?)
( ) 2 f x x = +(...) notations used in these notes are different than
notations used in your textbook. (...) a x. a x. a x a. b x. b x. b x
b. N x. f x. D x. n (...)/Asymptotes
Polynomial Functions
the graph of f (x) = mx + b by plotting two points and connecting them
with a line. (...) 2 = a. is a di(ff)erent problem from (fi)nding a
since our convention is that (...)
(f) A class of quadratic APN binomials inequivalent to power
functions every a = 0 and every b in F. n. 2 , the equation F (x)+F (x
+a) = b admits at most two (that is, (...) two di(ff)erent functions
from Table 1 to each other. We (...) Basics - Recursive Types: rec(X.F
(X))if A B then F(A) F(B), where Def S T == x:S. x T (...) Functions
over recursive types are usually themselves recursive. See Recursive
Functions. (...)
I hope you have not cursed both me and your cousin (at this point I
assume you have more than enough good cause to do so for my actions
are like being showered in the face with a confetti produced by place
a calc III text into a paper shredder including the illustrations and
their graphs and the equations all chopped into a 'wonderful math
salad' as Martha Stewart might say
I really like the simplicity of number four and want to know if itRG: It seems incomplete. I'm not sure what a(x) and b(x) are.
might be a (valid) statement to say:
MM: It does seem incomplete does it not? But is it incomplete if we
define a(x) and b(x) as (...)
RG: Ramona
MM: Martin(g)
Hot potato!
MM: + e - y = Dan Quale (sp?)
Profile of the 44th Vice President of the United States (...) student
William Figueroa's correct spelling of "potato" to "potatoe" at an
(..) -e + y = Dan Quayle [amongst all other known variables based on
the set of information we have contained].
MM: The hope i(s) we have expressed (x) the idea we have tried to
contain in language.
(But if we inverse)x(ample)s
The language i(n) which we have contained (x) the idea the hope i
(s) it has been expressed and the assumption is it is contained by
language. -easy
Form X to Y
N + X to Y
X to Y - N
From Y to X + N
(Or something similar as I do not know all the implications of the
letters entirely yet...)
.
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