- mathematics,
infinitesimal means infinitely small,
smaller than any
standard real number.
Infinitesimals are
often compared to
other infinitesimals of similar...
-
generalizations of
arithmetic operations.
Originally called infinitesimal calculus or "the
calculus of
infinitesimals", it has two
major branches,
differential calculus...
- mathematics, the term
infinitesimal generator may
refer to: an
element of the Lie algebra, ****ociated to a Lie
group Infinitesimal generator (stochastic...
- mathematics, an
infinitesimal transformation is a
limiting form of
small transformation. For
example one may talk
about an
infinitesimal rotation of a rigid...
- or
infinitesimal numbers. The
standard way to
resolve these debates is to
define the
operations of
calculus using limits rather than
infinitesimals. Nonstandard...
-
interpreted as
infinitesimals.
There are
several methods of
defining infinitesimals rigorously, but it is
sufficient to say that an
infinitesimal number is...
- &1\end{bmatrix}}.} The com****tion
rules for
infinitesimal rotation matrices are as
usual except that
infinitesimals of
second order are
routinely dropped....
-
differ in
magnitude from
other infinite quantities, and
infinitesimals from
other infinitesimals. Similarly, the
casual use of 1/0 = ∞ is invalid, since...
-
explicit use of
indivisibles (indivisibles are
geometric versions of
infinitesimals). The work was
originally thought to be lost, but in 1906 was rediscovered...
-
theory of
smooth infinitesimal analysis one can
prove for all
infinitesimals ε, NOT (ε ≠ 0); yet it is
provably false that all
infinitesimals are
equal to...
