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For more than a century, the academic community has been concerned with the training of Mathematics teachers, which often takes place isolated from the practice of basic school classrooms. When it comes to irrational numbers, the situation is no different. With a view to changing this scenario, we aim, in this experience report, to promote a debate on the content knowledge of irrational numbers, based on the reading of specific texts and a didactic activity with students from a public university. The work was conducted with seventeen students of the subject "Mathematics at School", of which fifteen were undergraduates and two were studying for a bachelor's degree. In two days of intervention, the collaborative observation, and the written productions of the students in the proposed activities were constituted as instruments for data collection. natural, integer and rational. Thus, we unveil such epistemological heterogeneity and warn that this, when not observed, can cause difficulties in student learning in Basic Education. [ABSTRACT FROM AUTHOR]

CPC 25 (2009) is the main accounting standard in Brazil that deals with contingent gains and it presents the disclosure requirements of these contingencies. This standard does not give the contingent asset item the same level of detail as it gives contingent liabilities and provisions. There are academic studies that have shown that: (i) this issue is controversial, (ii) the identification of a contingent asset is not an easy task, (iii) companies do not usually disclose their active contingencies, (iv) the values of the contingent gains can reach numbers of billions of Reals and (v) the Brazilian Securities and Exchange Commission (CVM) ordered the restatement of the financial statements of companies due to undue accounting of contingent gains. Considering this information, the objective of this research was to (a) analyze the adherence to CPC 25 (2009), regarding the disclosure of the contingent gains of the companies of the cyclical and non-cyclical consumer sectors listed on the BM&FBovespa and (b) propose a flowchart to assist companies and general accountants in the accounting treatment of contingent assets. The results of the analysis showed that 73% of companies did not meet contingent asset disclosure requirements, while 6% partially responded and only 21% were fully compliant with CPC 25 (2009). The low level of adherence to the standard evidences the need for additional clarification in CPC 25 (2009) and in the accounting literature in general. In presenting the proposed flowchart for accounting treatment of contingent gains, this study aims to make a direct and applied contribution to the corporate and academic world in order to aid in the improvement of the disclosure of contingent gains. Additionally, it was verified that the total estimated contingent assets disclosed exceeded R $ 6 billion. The present study is classified as an applied, descriptive, qualitative, quantitative, bibliographical and documentary research. [ABSTRACT FROM AUTHOR]

The set of real numbers, R, is a delicate issue to be addressed in the classroom. In particular, the study of the set of irrational numbers is hampered by lack of examples found in many textbooks. The main goal of this paper is presenting of clear manner an important example of irrational number: Euler's number. Here we present the motivation for the Euler's number as well, the proof of their irrationality. [ABSTRACT FROM AUTHOR]

The set of real numbers, ℝ, is a delicate issue to be addressed in the classroom. In particular, the study of the set of irrational numbers is hampered by lack of examples found in many textbooks. The main goal of this paper is presenting of clear manner an important example of irrational number: Euler's number. Here we present the motivation for the Euler's number as well, the proof of their irrationality. [ABSTRACT FROM AUTHOR]

The set of real numbers, R, is a delicate issue to be addressed in the classroom. In particular, the study of the set of irrational numbers is hampered by lack of examples found in many textbooks. The main goal of this paper is presenting of clear manner an important example of irrational number: Euler's number. Here we present the motivation for the Euler's number as well, the proof of their irrationality. [ABSTRACT FROM AUTHOR]

The concept of distance has a main importance to Science. Basically, if one can translate such notion into mathematics, the concept of distance is defined by a function whose arguments are pairs of real numbers and values are real numbers. Such conception of distance (metric space) is present in every realm of Physics, and finds its foundation on the intuitive idea that the distance between two points is the size of a continuous path that links these points. This article presents a new concept of distance, which one is built upon transreal numbers, a new domain of numbers created by the english computer scientist James A.D.W. Anderson. This new conception of metric space (transmetric space) allows the introduction of infinite distances, as well as distances between points which there is not any continuous path (metaphorically, a distance whose image is the "jump"). [ABSTRACT FROM AUTHOR]

It is well known that the field of real numbers, (ℝ, ≤), is an ordered, set and field, by the usual order (ℝ, +,., ≤). In this we show that the set of complex numbers, C, can be ordered. However, the complex field (..., +,.) can not be ordered. [ABSTRACT FROM AUTHOR]