… In the first half I concentrate on the need to prove felt by students engaged in
mathematical activity. In the second half I consider the need to prove on a societal level …

… First, we examine the close connection between the functions of proof within … the epistemology
of proof in the history of mathematics in order to elucidate the needs that propelled the …

… The alleged loss of prime farmlands is, in the words of the late Julian Simon, “the most
conclusively discredited … Increasingly, the attack on sprawl is being justified by the need to achieve …

… of proof, namely proof as explanation, and then consider the implications of this view of
proof for the handling of proof in the … the proofs th:rt explain rather than those that only prove. …

… social and cultural environment, and of the need to … do need to ensure, however, that
students develop the ability to assess each step in a proof and make an informed judgment on the …

… , I examine the structure of proof used by the law for the … the selection of a standard of proof
is an essential part of that structure. Third, I argue that the law's formal structure for the proof …

… In addition, even those students that succeeded to function in the proving ritual were not …
saw the point of proving, and/or the need to prove, especially when the statement to be proved …

… believes in using the environment as … the population and we are increasingly working with
the most deprived and disadvantaged groups within society. These activities join together the …

… Note that in our examples, the choice of proof structure is guided by the logical form of the …
Then according to the formulas for x and y given in the proof, we would have x = 2b−1 = 24−1 …

… It is now becoming more common for projects to use formal notations to document specifications
and even designs, but this project is unusual in the scale of the proof work that has been …