Definition
Monotonicity
MWG - Definition 3.B.2
The preference relation /equation.png)
on X is monotone if x /equation001.png)
X and y /equation002.png)
x implies y /equation003.png)
x.
If /equation007.png)
is monotone, we may have indifferent with respect to an increase in the amount of some but not all commodities.
If some commodity in the bundle of y changes from x, but the bundle are still the same, then y /equation008.png)
x.
Strong monotonicity
It is strongly monotone if y /equation004.png)
x and y /equation005.png)
x imply that y /equation006.png)
x
Strong monotonicity says that if y is larger than x for some commodity and is no less for any other, then y is strictly preferred to x.
Note
For y x and y x as vector relationship, check frequently used symbols.