intersection
Graph of .
If we want to examine the domain number and its weird function value , then our
open interval idea is in trouble. There is no filled space to the right of in the domain
where we could carve out an open interval.
Actually, we don’t need it.
We just need the domain numbers that are close to .
We need all of the domain numbers that are close to our domain number under observation.
We don’t need all of the real numbers that are close to our domain number under observation. We just need the real numbers that are actually members of the domain.
Slight Modification
Remember, we are after some language that works ALL of the time, even for
endpoints.
“Space” will refer to domain space that exists “around” our domain number under
observation.
Language:
All of the domain numbers inside a -interval around
Notation:
Domain
The intersection picks out the numbers that are both in the -interval and in the
domain.
This actually fixes a hidden problem. If our expectations are disrupted by a missing
domain number, then we shouldn’t be including that number in our -interval.
However, if we stipulate that we are only looking at domain numbers inside the
-interval, then everything works.
Tools
We have our tools ready.
- Open intervals for space.
- -intervals for closeness
We are ready to begin our algebraic description of interrupted expectations in function values.
ooooo=-=-=-=-=-=-=-=-=-=-=-=-=ooOoo=-=-=-=-=-=-=-=-=-=-=-=-=ooooo
more examples can be found by following this link
More Examples of Space