The trichotomy property of real numbers states that, for any two real numbers a and b, exactly one of the following is true:
For any equivalence relation R on set A, the relation is trichotomous if for all x and y in A exactly one of
holds.A trichotomous relation is not symmetric, not reflexive, but is transitive.
Property | Equation | Description |
---|---|---|
Symmetric property | A trichotomous relationship is not symmetric. For example, the statement 3<3 is always false. | |
Reflexive property | A trichotomous relationship is not reflexive. For example, 3 is less than 4, but 4 is not less than 3. | |
Transitive property | A trichotomous relationship is typically transitive. For example, 3<4, 4<5, and 3<5. | |
Table 1 |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | Y |
Z | X |
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