Midpoints and Exact Points of Some Algebraic
... and the 2D-normalization function x= x2 þ y2 . A part of the results presented on division and square root have been known for some time in binary arithmetic; see, for instance, the pioneering work by Markstein [9], as well as studies by Iordache and Matula [6] and Parks [11]. Let us also recall the ...
... and the 2D-normalization function x= x2 þ y2 . A part of the results presented on division and square root have been known for some time in binary arithmetic; see, for instance, the pioneering work by Markstein [9], as well as studies by Iordache and Matula [6] and Parks [11]. Let us also recall the ...
Five regular or nearly-regular ternary quadratic forms
... to represent. Our methods are similar to those in [4]. A more recent article with a short history and bibliography of work on regular ternary forms is [3]. 2. Techniques. Our main tool is the relation of a form with diagonal forms of known behavior. For instance, with the form h above, we represent ...
... to represent. Our methods are similar to those in [4]. A more recent article with a short history and bibliography of work on regular ternary forms is [3]. 2. Techniques. Our main tool is the relation of a form with diagonal forms of known behavior. For instance, with the form h above, we represent ...
Values of the Carmichael Function Equal to a Sum of Two Squares
... holds with some absolute constant c1 > 0 for all sufficiently large values of x . Our proof of the upper bound of Theorem 1 (see Section 4) uses ideas from [1], where similar bounds have been obtained for the Euler function ϕ(n) and for the sum of divisors function σ(n). One difference in our case is t ...
... holds with some absolute constant c1 > 0 for all sufficiently large values of x . Our proof of the upper bound of Theorem 1 (see Section 4) uses ideas from [1], where similar bounds have been obtained for the Euler function ϕ(n) and for the sum of divisors function σ(n). One difference in our case is t ...
Syllogistic Analysis and Cunning of Reason in
... for instance tried to construct the whole mathematics by three mother structures, all three structures are defined by syllogisms. Some researchers in philosophy of mathematics use a special syllogism called complementarity in searching for mathematical knowledge. According to Otte, mathematical prac ...
... for instance tried to construct the whole mathematics by three mother structures, all three structures are defined by syllogisms. Some researchers in philosophy of mathematics use a special syllogism called complementarity in searching for mathematical knowledge. According to Otte, mathematical prac ...
Proof-Net Categories - Matematički Institut SANU
... theorem that 2 is not rational. There are, on the other hand, theorems that are more difficult to prove than to conjecture (and there are no doubt theorems were the conjecture and the proof are of equal difficulty). The results we are going to present are of a kind called in logic completeness theor ...
... theorem that 2 is not rational. There are, on the other hand, theorems that are more difficult to prove than to conjecture (and there are no doubt theorems were the conjecture and the proof are of equal difficulty). The results we are going to present are of a kind called in logic completeness theor ...
PERIODIC DECIMAL FRACTIONS A Thesis Presented to the Faculty
... must be obtained, say rh, that is either the same as one pre viously obtained, say rk' or equal to 1 (in which case k = 0). Note that the next digit in the quotient, namely ah+l' will necessarily be the exact digit that was acquired in the division after the remainder rk was obtained. ak+l' ...
... must be obtained, say rh, that is either the same as one pre viously obtained, say rk' or equal to 1 (in which case k = 0). Note that the next digit in the quotient, namely ah+l' will necessarily be the exact digit that was acquired in the division after the remainder rk was obtained. ak+l' ...
Mathematical proof
In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms. Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed true is known as a conjecture.Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.