Sentence examples for both types of proof from inspiring English sources
Both types of proof are thus based upon the principle of contradiction, and since the object of mathematics in general is magnitude and that of geometry in particular extension, one can say that in mathematics in general our concepts of magnitude are unpacked and analyzed, while in geometry in particular our concepts of extension are unpacked and analyzed.
-Are there certain types of proof that are more believable than others?
(See I.R.S. Publication 552 for a detailed rundown of the types of proof needed to verify various tax information).
The British Bankers Associationn says that in these cases banks and building societies have procedures that allow them to accept other types of proof such as a tenancy agreement or a letter from an employer.
Of these, the best-known is the intuitionistic calculus, devised by Arend Heyting, one of the chief representatives of the intuitionist school of mathematicians, a group of theorists who deny the validity of certain types of proof used in classical mathematics (see mathematics, foundations of: Intuitionistic logic).
Numismatist Paul Green ascribed the two varieties to the two types of proof sets that the Mint sold at the time that would have contained the two-cent piece.
The types of proof required and accepted vary by state and by jurisdiction.
The types of proof sets that are available depend on the year the coins were issued.
Bolzano's problem is that of providing precise criteria for distinguishing the two types of proofs.
