We put b in R unless a is already in.
This equation has a solution in integers provided that N>7.
Expand f in powers of x.
It is this point of view which is close to that used in C*-algebras.
These intervals are disjoint from all those used in defining J1.
Each Ai meets A in a finite set. [= Ai∩ A is finite]
Then one Yi can intersect another only in one point.
Values computed for the right side of (2) were rounded up in the fourth decimal place.
Then F varies smoothly in t.
Thus Fn(x,y) converges to F(x,y) uniformly in x.
Clearly, Aj is increasing in j.
The word ends in a.
in diagonal form
in geometric language
In less precise language, the requirement is that the two angles are the same in size and in orientation.
Then P is the product of several integer factors of about xn in size.
The set A is roughly triangular in shape.
The proof proper [= The actual proof] will consist of establishing the following statements in sequence.
convergence in probability <in distribution>
Less than 1 in p of its points will result in a quartic with ideal class number p.
Theorem 3 is remarkable in that considerably fewer conditions than in the previous theorems ensure universality.
As M is ordered, we have no difficulty in assigning a meaning to (a,b).
The prime 2 is anomalous in this respect, in that the only edge from 2 passes through 3.
This is where the notion of an upper gradient comes in.