Mathematical English Usage - a Dictionary

by Jerzy Trzeciak

follow

[see also: imply, ensuing, subsequent]

The remarks following Theorem 2 show that $a=0$.

The analysis to follow only covers the case $d=1$.

We make the following provisional definition, which is neither general nor particularly elegant, but is convenient for the induction which is to follow.

The following three statements are equivalent: ......

For $D$ a smooth domain, the following are equivalent.

The following has an almost identical proof to that of Lemma 2.

The idea of the ensuing computations is the following: ......

His argument is as follows.

The fact that the number $T(p)$ is uniquely defined, even though $p$ is not, enables us to define the nullity of $A$ as follows.

In what follows $\langle$In all that follows$\rangle$, $L$ stands for ......

Throughout what follows, we shall freely use without explicit mention the elementary fact that ......

It follows that $a$ is positive. [= Hence $\langle$Consequently,/Therefore,$\rangle$ $a$ is positive.]

Firstly, if $G$ is abelian, does it follow that $S(G) = K$, or equivalently, that $X_G = p(M(G))$?

If we prove that $G>0$, the assertion follows.

The general case follows by changing $x$ to $x-a$.

We follow Kato [3] in assuming $f$ to be upper semicontinuous.

Following the same lines we find that it takes $k$ prolongations to get an immersed curve.

The proof follows very closely the proof of (2), except for the appearance of the factor $x^2$.

It is intuitively clear that the amount by which $S_n$ exceeds zero should follow the exponential distribution.



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