Mathematical English Usage - a Dictionary

by Jerzy Trzeciak

know

[see also: realize, recognize, grasp, aware]

We do not know whether or not $Q(R)=R$ in this situation.

The map $f$, which we know to be bounded, is also right-continuous.

Knowing this matrix is equivalent to knowing the multiplicities of the $k_i$.

However, we know of no way of deriving one theory directly from the other.

All the Cox maps $F$ are known to have $L(F)$ finite.

The best known of these is the Knaster continuum.

The answer is not known to us.

The only references known to the authors are [A] and [V], where the case $A=L(E)$ is settled in the negative.

Many of them were already known to Gauss.

It has long been known that ......

It has been known for some time that ......

The conjecture (now known not to be true in general) was that ......

So far it seems not to be known whether the geometric condition on $X$ can be omitted.

In particular, there is a summary of what is known about polarized pairs with small genus.

The importance of these examples lay not only in lowering the dimension of known counterexamples, but also in ...... [Note that the past tense of lie is lay, not “lied”.]

The following proposition is probably well known, but we do not have a reference.



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