## Research Proposal – Teaching of infinity

Studies about the teaching of infinity demonstrated that understanding any forms of infinity requires understanding of some mathematical concepts such as the successor principles and the basic metaphor of infinity. More generally, mastering (even fractionally) certain fields of mathematics such as geometry, algebra, and arithmetic’s is paramount to understand vastness. Other explanations, such as empirical, of infinity would be pointless since vastness is in nature abstract and mathematics is the science of the abstract. The main aim of this research paper will be to explore the devices through which mathematics explain infinity. In order to pursue this inquiry, we need to answer some questions. What fields of mathematics can explain the concept of vastness? How does the properties of those fields explain infinitude? The importance of those questions lies in the fact that they help us tackle the core of the relationship between infinity and mathematics.

### Further Description

Those questions are also adequate, since they help us narrow the field of our research. Answering those questions will be arduous. In fact, experimenting will be impossible given the abstract nature of our subjects. We will then use only exploratory and explanatory research. Exploratory research to propose original answers to our questions and explanatory research to elaborate on the points made by the sources we will use. The sources that will be used in order to explore the questions we formulated will mainly be scholarly articles, books, and other kinds of publications in mathematics, more specifically in algebra, geometry, and arithmetic’s. Sources such as surveys or experiments would be obsolete once again, given the abstract nature of mathematics and infinitude.

Researching those questions can only give us a biased interpretation of infinity. First there is the problem of the empirical explanation of infinity. Even though infinity in inherently abstract and not perceivable through senses, one could argue that the notion of actual infinity gives empiricists a possibility of explaining infinitude. The, the problem of broadness arises. Mathematics are broad and identifying mathematical devices in only some fields would be prejudicial to the other branches. Despite those concerns, the formulated questions will give us proper answers regarding mathematics approach of infinity.

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