[see also: selection]
Thus $F$ is independent of the choice of the family $S$.
Indeed, it is routine to verify that the index so constructed is independent of the choices made.
We do not know how $V$ depends on the various choices made.
The choice of $A$ is clearly irrelevant, so assume $A=0$.
Our choice of $V$ shows that ......
With this choice of $b$, ......
For this choice of $\alpha,\beta$ and with $u=z=s$, the expression (5.3) simplifies greatly.
Corresponding to each choice of $V$ there is a function $f$ such that ......
The problem is that, whatever the choice of $F$, there is always another function $f$ such that ......
This just amounts to a choice of units.
By choice of $V$, ......
Having established (1), one might be tempted to try to extend this result to general $p$ through the choice of a suitable ideal $B$.
There are $O(1)$ possible choices for $x$.
Where there is a choice of several acceptable forms, that form is selected which ......
It is the freedom of choice of $D$ in this construction that enables us to ......
On the other hand, there is enormous ambiguity about the choice of $M$.
In order to carry out the construction, we must make a judicious choice of $P$.
By revising our choice of $A$ if necessary, we may assume that ......
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