Do any theorems of analysis have proofs in which diagrams have a non-superfluous role?
For this reason it has been widely thought that, beyond some very simple cases, arguments in real and complex analysis in which diagrams have a non-superfluous role are not genuine proofs.
Between the extremes we find the view that, even if no picture alone is a proof, visual representations can have a non-superfluous role in reasoning that constitutes a proof.
But developments in the Soviet Union soon made his role superfluous, and at the same time Lech Walesa, the Solidarity leader, was pressing hard for his job.
Also, while along with deep myometrial invasion, tumor size as well as lymph node metastasis (LNM) can be assessed with MRI, it is limited in its capacity in detecting LNM, which led some authors to consider its role superfluous [ 74] or simply suggesting it should not be performed [ 75].
(Alistair) Looking ahead, the aim shared by many participants was to make their role superfluous so that, as Desmond states, 'if we walked away or got run over by a bus it would continue': One of the things we always try to do … is to understand when we can disappear, because ultimately what we are trying to do is to do ourselves out of a job here.
Smiley recreates in meticulous detail the limited prospects society at this time offered women: bred to be wives and mothers, they are regarded as dangerously superfluous if those roles fail to materialise.
A lot of people who now make a living in the middle will find their roles superfluous.
Her role is superfluous to the construct of the story, and she is never completely believable as one who would show this kind of support.
Try to stand in the shoes of those who are viewing the writing role as superfluous or easily outsourced.
It has been considered as relatively superfluous apart from its supporting role amongst more specialized tissues [ 1].
