Sentence examples for we shall sometimes from inspiring English sources

We shall sometimes refer to elementary type theory as T .

We shall sometimes use X ≲ Y to denote the estimate X ≤ C Y for some C.

In what follows, we shall sometimes use the variables m, n, and o to range over the natural numbers.

If (Omega ) is bounded we shall sometimes write (H^1_0(Omega )) instead of (D^{1,2}(Omega )).

We shall sometimes use the notation (A lesssim B) instead of (A leq CB), and (Aapprox B) means that (A lesssim B ) and (Blesssim A).

We shall sometimes remark on the differences between the calculus presented below and the calculus that Frege developed, but such remarks are not intended to be a scholarly guide to the many subtleties involved in understanding Frege's original works.

We shall also sometimes use (V(rho)) to stand for (V_{rho}(0,1)).

We shall also sometimes treat indexing vectors such as W as sets such that n∈ W means that the node n is in the subsystem ψ W. In general, although we can specify the states of each node with this type of notation, an important ambiguity remains because information about the network structure is not included.

end{aligned}   (4) If G is a subset of ({{mathrm{text {Aut}}}}(X)), then the natural marked variety is the triple (X, G, i), where ( i :G rightarrow {{mathrm{text {Aut}}}}(X)) is the inclusion map, and it shall sometimes be denoted simply by the pair (X, G).

Meaningful lives are not so limited and, as we shall see, are sometimes more vexed.

Such a simplex is an n-dimensional object and we shall call it sometimes an n-simplex if we would like to emphasize its dimension.