最終更新日:2022/12/24
As mentioned earlier set theory provides a general conceptual framework for mathematics. Now, since category theory, through the notion of topos, has succeeded in axiomatising set-theory, the outcome is an entirely new categorial foundation of mathematics! The category-theorists attitude that function
rather than set membership
can be seen as the fundamental mathematical concept has been entirely vindicated. The pre-eminent role of set theory in contemporary mathematics is suddenly challenged. A revolution has occurred in the history of mathematical ideas (albeit a peaceful one) that will undoubtedly influence the direction of the path to the future.
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元となった例文
As
mentioned
earlier
set
theory
provides
a
general
conceptual
framework
for
mathematics.
Now,
since
category
theory,
through
the
notion
of
topos,
has
succeeded
in
axiomatising
set-theory,
the
outcome
is
an
entirely
new
categorial
foundation
of
mathematics!
The
category-theorists
attitude
that
"function"
rather
than
"set
membership"
can
be
seen
as
the
fundamental
mathematical
concept
has
been
entirely
vindicated.
The
pre-eminent
role
of
set
theory
in
contemporary
mathematics
is
suddenly
challenged.
A
revolution
has
occurred
in
the
history
of
mathematical
ideas
(albeit
a
peaceful
one)
that
will
undoubtedly
influence
the
direction
of
the
path
to
the
future.