Sentence examples for greatest lower from inspiring English sources

And in any case how does one decide whether points on a line have a greatest lower bound?

He defined the real numbers to be the cuts (L, U) just described that is, as partitions of the rationals with each member of L less than every member of U. Cuts included representatives of all rational and irrational quantities previously considered, but now the existence of greatest lower bounds became provable and hence also the intermediate value theorem and all its consequences.

Bolzano also relied on an assumption the existence of a greatest lower bound: if a certain property M holds only for values greater than some quantity l, then there is a greatest quantity u such that M holds only for values greater than or equal to u. Bolzano could go no further than this, because in his time the notion of quantity was still too vague.

To see that is the greatest lower bound of, assume that some satisfies for all.

We denote by d ( x, T y ) the greatest lower bound of W x ( T y ).

Denote d ( x, T y ) by the greatest lower bound of W x ( T y ).

Remark 2.1 (Estimate of the greatest lower bound of the spectrum).

Let λ 0 be the greatest lower bound of spectrum of the operator ℒ.

Let λ 0 be the greatest lower bound of the spectrum of ℒ.

Denote by tau = text{the greatest lower bound of the set of possible values of}~a_{0}~text{satisfying} (14).

where denotes the infimum or the greatest lower bound of the activation function, and is a small positive constant.