"tends to zero" is correct and usable in written English.
You can use it to express the concept of decreasing toward zero. For example, "As the temperature decreases, the pressure of the gas tends to zero."
Thus Φ is O for codes with K = 20, and Φ tends to zero if ε tends to zero.
Since is also arbitrarily small provided that the number is small enough, the right of (5.12) then tends to zero independent of as tends to zero.
and taking its limit as h tends to zero.
Obviously, the area of this Sierpinksi carpet tends to zero as n tends to infinity.
Taking the limit as h tends to zero, the result follows.
This scheme does not degenerate when the body thickness tends to zero.
In particular, the solution tends to zero in the supremum norm.
Even though dm/dt never tends to zero, it is always small relative to the production and loss rates.
It is well known that one obtains a diffusion problem as ϵ tends to zero.
We discuss first the limit equations for this case, when the Mach number tends to zero.
The pressure tends to zero.
