Continuity was necessary for Leibniz's infinitesimal calculus.

Although at first it might seem to rule out QM, and it would be problematic for
atomic structures,  but in these it only applies to particles. The 
quantum wave field is a probability field which is smooth and continuous.

"Principle of Continuity

According to Leibniz, there are “two famous labyrinths where our reason very 
often goes astray.” 
(G VI 29/H 53)  The first concerns human freedom, the latter the composition of 
the continuum. 
Leibniz, however, thought  that he had found the way out of each labyrinth, and 
his solution 
to the problem of the continuum is related  ultimately to a maxim or law that 
he employs not 
only in his mathematical writings but also in his metaphysics. As he puts it in 
the Preface to 
the New Essays, “Nothing takes place suddenly, and it is one of my great and  
best confirmed 
maxims that nature never makes leaps.” (A VI vi 56/RB 56) More exactly, Leibniz 
that this law or principle implies that any change passes through some 
intermediate change 
and that there is an actual infinity in things. The Principle of Continuity 
will be employed to 
show that no motion can arise  from a state of complete rest and that 
“noticeable perceptions 
arise by degrees from ones which are too minute to be noticed.” (ibid.)"

Dr. Roger B Clough NIST (ret.) [1/1/2000]
See my Leibniz site at Roger Clough
DreamMail - Your mistake not to try it once, but my mistake for your leaving 
off. use again

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