interval
intervals... defined on a dense set of numbers. daamath provides a few important functions for interval
with one point A, we have three regions of the 1D real number line, and thus 2 ^ 3 = 8 possible functions:
| < A | A | A < | name |
|---|---|---|---|
| F | F | F | |
| F | F | T | gt |
| F | T | F | eq |
| F | T | T | ge |
| T | F | F | lt |
| T | F | T | ne |
| T | T | F | le |
| T | T | T |
functions that involve more than one point can be composed of any of these, but for convenience, daamath provides the following:
with two points A and B, we have five regions of the 1D real number line, and thus 2 ^ 5 = 32 possible functions:
| < A | A | A < & < B | B | B < | name |
|---|---|---|---|---|---|
| F | F | F | F | F | |
| F | F | F | F | T | |
| F | F | F | T | F | |
| F | F | F | T | T | |
| F | F | T | F | F | oo |
| F | F | T | F | T | ? |
| F | F | T | T | F | oc |
| F | F | T | T | T | |
| F | T | F | F | F | |
| F | T | F | F | T | ? |
| F | T | F | T | F | ? |
| F | T | F | T | T | ? |
| F | T | T | F | F | co |
| F | T | T | F | T | ? |
| F | T | T | T | F | cc |
| F | T | T | T | T | |
| T | F | F | F | F | |
| T | F | F | F | T | ncc |
| T | F | F | T | F | ? |
| T | F | F | T | T | nco |
| T | F | T | F | F | ? |
| T | F | T | F | T | ? |
| T | F | T | T | F | ? |
| T | F | T | T | T | |
| T | T | F | F | F | |
| T | T | F | F | T | noc |
| T | T | F | T | F | ? |
| T | T | F | T | T | noo |
| T | T | T | F | F | |
| T | T | T | F | T | |
| T | T | T | T | F | |
| T | T | T | T | T |
daamath only defines these on 1D spaces for now, and does not define intervals or regions for 2D spaces such as complex numbers and such
API implementation
lt(a, b):
less than
a < b
le(a, b):
less than or equal to
a ≤ b
eq(a, b):
equal
a = b
ne(a, b):
not equal
a ≠ b
ge(a, b):
greater than or equal to
a > b
gt(a, b):
greater than
a ≥ b
oo(x, a, b):
in open interval
x ∈ (a, b)
oc(x, a, b):
in left-open interval
x ∈ (a, b]
co(x, a, b):
in right-open interval
x ∈ [a, b)
cc(x, a, b):
in closed interval
x ∈ [a, b]