[see also: stroke] Its role is to rule out having two or more consecutive P-moves (on the grounds that they can be performed in one go).
[see also: continue, proceed, pursue, turn] a path obtained by going from A to B along the lower half of the circle
Here the interesting questions are not about individual examples, but about the asymptotic behaviour of the set of examples as one or another of the invariants (such as the genus) goes to infinity.
We adopt the convention that the first coordinate i increases as one goes downwards, and the second coordinate j increases as one goes from left to right.
Some members go into more than one Vk.
To go into this in detail would take us too far afield.
We now go through the clauses of Definition 3.
Before going to the proof, it is worth noting that......
This idea goes back at least as far as .
This argument goes back to Banach.
Going back to the existential step of the proof, suppose that......
Before we go on, we need a few facts about the spaces Lp.
The equation PK=0 then goes over to QK=0.
The rest of the proof goes through as for Corollary 2, with hardly any changes.