The concept of a quantum dot in the island formula is a region of spacetime that is disconnected from the boundary, but is still encoded in the boundary theory.
Limits (Formal Definition)
Approaching ...
Sometimes we can't work something out directly ... but we can see what it should be as we get closer and closer!
Example:
(x2 − 1) (x − 1)
Now 0/0 is a difficulty! We don't really know the value of 0/0 (it is "indeterminate"), so we need another way of answering this.
So instead of trying to work it out for x=1 let's try approaching it closer and closer:
Let's work it out for x=1:
(12 − 1) (1 − 1) = (1 − 1) (1 − 1) = 0 0
Example Continued:
| x |
|
(x2 − 1) (x − 1) |
| 0.5 |
|
1.50000 |
| 0.9 |
|
1.90000 |
| 0.99 |
|
1.99000 |
| 0.999 |
|
1.99900 |
| 0.9999 |
|
1.99990 |
| 0.99999 |
|
1.99999 |
| ... |
|
... |