INFINITIVE AND GERUND
Adapted from Trzeciak Jerzy, Writing Mathematical Papers in English. European Mathematical society, 1995 Infinitive a) Indicating aim or intention
b) In constructions with too and enough
c) Indicating that one action leads to another
d) In constructions like "we may assume M to be......"
e) In construction like "M is assumed to be......."
f) In the structure "for this to happen"
g) As the subject of a sentence
h) After forms of "be"
Í) With nouns and with superlatives, in the place of a relative clause j) After certain verbs (lead, claim, turn out, appear, need, make)
ing-form a) As the subject of a sentence
b) After prepositions (after, on, in, instead of, besides, for, etc.)
c) In certain expressions with "of
d) After certain verbs, especially with prepositions (begin, succeed, persist, result, put off, worth noting, merit, etc)
e) Present Participle in a separate clause (subjects of the main and subordinate clause are the same)
f) Present Participle describing a noun
g) In expressions which can be rephrased using "where" or "since"
h) In expressions which can be rephrased as "the fact that X is......"
Exercise. Fill in the spaces with infinitive or gerund forms of verbs.
1) We define K.........the section of H over S. (be)
2) After............a linear transformation, we may assume that (make)
3) We use the technique of.................(extend)
4) After having finished............(2), we will turn to (prove)
5) We need only consider paths.............at 0. (start)
6) ..........that this is not a symbol is fairly easy, (see)
7) For this............, F must be compact. (happen)
8) Instead of..........the Fourier method we can multiply (use)
9) Actually, Shas the much stronger property of...........convex, (be)
10).................proposition 5 and Theorem 7 gives (combine)
11) Note that M........cyclic implies F is cyclic. (be)
12)..................this to R, we can define (restrict)
13) We put off............this problem to Section 5. (discuss)
14) Now, F..........convex, we can assume that (be)
15) This map turns out.............. (satisfy)
16) We need............the following three cases, (consider) •<
17) The problem here is..................... (construct)
18) The map M is assumed................open. (be)
19) We now apply (5)...........an x with norm exceeding 1. (obtain)
20) This case is important enough..........separately, (be stated)
21) We make G.........trivially on V. (act)
22) These properties led him.............that (suggest)
23) He proposed..........that problem. (study)
24).............the previous argument and using (3) leads to (repeat)
25) We begin by..............(3). (analyze)