[see also: consequently, hence, thus, therefore, way]
Indeed, it is routine to verify that the index so constructed is independent of the choices made.
The constants are so adjusted in (6) that (8) holds.
......where $C$ is so chosen $\langle$chosen so$\rangle$ that ......
The control problem is to choose an investment strategy so as to minimize ......
The first of these was suggested by J. Serrin, who showed how to modify my earlier treatment of ...... so as to obtain stronger results with no extra effort.
The ordered pair $(a,b)$ can be chosen in 16 ways so as not to be a multiple of $(c,d)$.
Thus $A$ is compact, and hence so is $B$.
Consequently, $A$ is compact. Therefore, so is $B$.
Since $R$ is polynomial in $x$, so also is $P$.
We have been working under the assumption that ...... Suppose now that this is no longer so.
If this is so, we may add ......
If this is not so, a linear fractional transformation will make it so.
Then $F$ is bounded but it is not necessarily so after division by $G$.
We will want to prove that ...... To do so, we will need to define ......
A geodesic which meets $bM$ does so either transversally or ......
This shows that the sequence (1) is bounded below, and so the definition of $L(f)$ is meaningful.
Then $a=b$, so that $f$ is not injective.
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