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Analytic Proof Homework Help


In mathematics, it is the fundamental theory of bringing the similarities between a numbers of proofs, to define the structural proof theory. Sowder classifies these types of proof as: Transformation Proofs and Axiomatic Proof. In general, one would not disagree with this given classification. As one cannot prove the contrary- namely that are there are other types of proofs.


Transformational Proof

This type of proof is an argument appropriate to the problem but the set, often in a more general con text. As an example, Let us show that f(n)=n^2-79n+1601 is not always a prime for all sufficiently large n.

Let N be an integer greater than 79 and x > N.

f(x)=x^2-79x + 1601 = y, say.

Note that y > 1 (why?)

f(ry+x) = (ry+x)^2 - 79(ry+x) + 1601 which is divisible by y for every integer r (why?).

Therefore, since f(ry+x) tends to infinity with r, there are infinitely many composite values of f(n).

The level of technique would provide the solution by using this type of proof did not call in any axioms or theorems except a fact that can be used without explicit mention, namely, that a product of integers is indeed divisible by the factors of the multiplicands. Thus in mathematics many of the proofs does require the solution using transformational proofs.


Axiomatic Proof

This is the process by which one proves-irrefutably establishes-Nothing but the result by calling in present assumptions, to the prior results; it is perhaps the most distinguishing aspect behind a mathematical theorem or proposition, without it the statement of the theorem would remain a conjecture. To understand this type more clearly we can consider the most famous math’s book- The Elements by Euclid. Here, we may find more than 400 propositions and each proof in the Elements is an axiomatic proof. The ordering the wording are carefully made in the axiomatic proof. The two-column in geometry is an example of this type.

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