Mathematical English Usage - a Dictionary

by Jerzy Trzeciak


[see also: suppose, presume]

Here $F$ is assumed to be open. [ But: We assume that $F$ is open, not: “We assume $F$ to be open”.]

......, the limit being assumed to exist for every real $x$.

The assumed positivity of $u_n$ is essential for these results.

We can assume, by decreasing $n$ if necessary, that ......

We may (and do) assume that ......

We tacitly assume that ......

It is assumed that ......

We follow Kato [3] in assuming that $f$ is upper semicontinuous.

The reader is assumed to be familiar with elementary $K$-theory.

Then $X$ assumes values $0,1,...,9$, each with probability $1/10$.

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