Mathematical English Usage - a Dictionary

by Jerzy Trzeciak

out

Choose one out of these ten.

in nine cases out of ten

Define $a_k$ to be the probability that exactly $k$ out of the $2n$ values $X_i$ exceed $T$, conditional on $X_0>T$.

The only edges out of 3 lead to 2 or into $B$.

It is clear that (up to set-theoretic niceties) this defines a partial order on the class of $R$-equivalence classes of Borel maps out of the given space $X$.

A second technique for creating new triangulations out of old ones is central retriangulation.

The detailed analysis of ...... is carried out in Section 2.

This term drops out when $f$ is differentiated.

We were surprised to find out that ...... $\langle$at finding out that ......$\rangle$

This accords with the intuition that as we pass down the coding tree, we find out more and more detailed information about the ordering actually represented.

Our study grew out of some valuable conversations with Kirk Douglas.

We lay out the details of this generalization in the first part of this paper.

The image of $U$ under $f$ misses out more than three points of the sphere.

Then $A=B$, as one sees by multiplying out the product on the right.

One unusual feature of the solution should be pointed out.

To round out the picture presented by Theorem 5, we mention the following consequence of ......

The possibility $A=B$ is ruled out in the same way.

By modifying the technique set out [= presented] in [3], we obtain ......

With this definition of a tree, no vertex is singled out as the root.

It turns out that these properties play no role in the proof.

By writing out the appropriate equations, we see that this is equivalent to ......



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