Sentence examples for various proofs from inspiring English sources

In collating, you used a pencil to carefully transfer changes from various proofs from the editor, the author, the proofreaders (usually two), the lawyer, and the fact checker onto a clean proof for the printer.

The exponential inequality plays an important role in various proofs of limit theorems.

Le Grand responded to Parker's charges of atheism in his Apologia de Descartes (1679), challenging Parker's criticisms with various proofs of God's existence.

It is well known that the probability inequality plays an important role in various proofs of limit theorems.

Since the appearance of this inequality various proofs and generalizations or improvements have appeared in the literature for different types of differential equations.

In the subsequent papers, various proofs and reformulations of this inequality have been presented, we refer to [2, Chapter XIII], and to [3 5] for some details.

These include the systematic design of semantics modeling various proof methods and the characterization of assertions as abstract domains.

These games are a useful device for showing upper and lower bounds on the lengths of proofs in various proof systems.

Various further proofs have since been given, but these proofs generally require extensive prior subject knowledge in order to follow them, or are 'blind' proofs in the sense that most of the work is done by computer or by exhaustive enumeration.

For certain graphs, various found proofs will share common subsets, which are simulated redundantly.

Mordell and Barrow [2] first proved it in 1937, and since then this inequality is known as the Erdös-Mordell inequality and has attracted the attention of many mathematicians who offered various new proofs, generalizations, variations, sharpness, and conjectures (see [3 33] and the references therein).