Numbers and numerals
There is a lot of confusion that arises when it comes to numbers and numerals. In detail, the two concepts may be related to some point, but have an ideal difference. In brief, one may consider the written idea as numerals, but a lot of people confuse it with numbers. In essence, a number is anything that we talk about in mathematics, such as “four,” which may be very difficult to understand. In reality, it is considered an abstract.
On the other hand, a numeral is related to any symbol for a specific number. For instance, the binary symbol 0101 is considered a numeral (Crall par.4). The focus of this paper is to elucidate the differences that exist between numbers and numerals. It goes ahead to look at how this distinction helps to enumerate the mathematical Platonism.
In a real sense, a number related to a diverse set of arithmetic operations through various operation occurs. For instance, the incorporation of integers, fractions, and complex numbers (Crall par.2). In addition to the above notion, numbers encapsulate different conventional symbols that one name may include another number system. Numerals, on the other hand, define different symbols that complement numbers. In other words, numerals iterate through numbers to form a conjoined meaning of numbers.
In most cases, this is usually done in writing mode. The use of non-conventional notation is a perfect example of this construct. It means that there are a lot of distinctions that are alienated to numbers and numerals as well.
Moreover, there are different forms in which the distinction between numbers and numerals relates to mathematical Platonism and realism. A lot of research done to differentiate numerals and numbers are geared towards making an analogy on the mathematical Platonism (Eugene, and Judson par.4). A typical manifestation of this theory places its baseline on the realism of life. While these aspects may be different, mathematical concepts quantify and describe numbers and numerals on a diversified platform. These analogies, according to Platonism, are incorporated and used in daily operations. In essence, mathematical Platonism combines any metaphysical account of mathematics. In doing so, it brings out the analogy that mathematical concepts can be used in the reality of life. The concept of realism in mathematics is elucidated through numbers and numerals. Aspects of normalcy and abstract in the daily application is related to the universality of life. Mathematical realism, on the other hand, quantifies the abstract and independent nature of numbers and numerals. For instance, Platonism stipulates how different aspects of numbers exist outside the confines of space. A case of lambda as a mathematical symbol that enumerates the different construct of numbers exists outside space and time. In doing so, it means that lambda has different characteristics regardless of the physical and mental surroundings. The human activities are well integrated with numerals and numbers. The abstract nature of numbers is often related to the realism of life. Characterization of Platonism requires an integration of a compact epistemology that affect how decisions are made. Their application, on the other hand, the distinction between numerals and numbers, gives a deep insight into abstract objects. This reality exists beyond the physical realm as it leads to the generation and understanding of mathematical concepts. The interrelation between Platonism and the distinction of numbers and numerals creates an analogy that mathematical abstract can be used to create thought, knowledge, and practices.