Sentence examples for must have finite from inspiring English sources

It was clear to Burnside that an infinite group (such as the positive integers) may have a finite number of generators and a finite group must have finite generators, but he wondered if an infinite group could result from using a finite set of generators, each of finite order.

Therefore (I) is finite and (R) must have finite uniform dimension.

Metastable states must have finite lifetime and the definition of state has to include a reference to time.

The assumption that the tuning curves must have finite support within the fundamental domain of the lattice corresponds to grid cells being silent outside of the firing field.

However, real detectors must have finite size and the point assumption is not exactly valid, which leads to limitations in the accuracy of the reconstruction.

As we have shown in [10], linearisability does not require confined singularities although the solutions must still have finite Nevanlinna order.

To be feasible in the laboratory, the optimal electric field must have a finite amplitude.

But if you have a definite number of things, he concludes, you must have a finite—'limited' number of them; he implicitly assumes that to have infinitely many things is to have an 'indefinite' number of them.

The additional qualification serves to make the distinction with Hilbert's finitism which, roughly speaking, can be seen as a form of finitism on the meta-level (e.g., although mathematical theories can talk about infinite structures, still the proofs in such theories must have a finite length).

This led Alhazen to propose that light must have a finite speed, and that the speed of light is variable, decreasing in denser bodies.

Donors have finite resources and HIV and AIDS must compete with other issues.