Sentence examples for of proofs that from inspiring English sources

Mathematics progresses by inventing new mathematical concepts that facilitate the construction of proofs that would be far more complex and even impossible without them.

Here's a sample proof in Mizar of the existence of a rational number xy where x and y are irrational: Examples of proofs that have been checked by Mizar include the Hahn-Banach theorem, the Brower fixed-point theorem, Konig's lemma, the Jordan curve theorem, and Gödel's completeness theorem.

The reality show theorem is a simple one: Propose a basic niche, and then go about a set of proofs that, with simple variations on a theme, repetitively reinforce it.

A natural question arises: "is there a representation of proofs that abstracts from such uninteresting details?".

Many difficult research results in logic become just exercises through the control over the structure of proofs that the G3-calculi permit.

As one of the proponents of the former, Oller (1979, 1983) reported a series of proofs that a single trait (Oller himself does not define what the trait is in a clear and consistent manner though) could explain the major portions (over 70%) of the total variance of various tests, including TOEFL PBT.

"You want some sort of proof that is you and isn't you," she admonishes me.

-Are there certain types of proof that are more believable than others?

We go for different kinds of proof, that depends on the wife.

Is the current standard of proof that must be met fair to students?

But doctors acknowledge the lack of proof that lower doses are safer.