Real Numbers are a core component of mathematics, having many applications in science, engineering, and everyday life. For anyone studying advanced math, understanding the real number system is essential. But what exactly is the real number system and how does it work? Well, this article will explain the structure of the real number system and provide a schematic diagram so you can get an easier visual understanding of this crucial mathematical concept.
The real number system is a mathematical concept that pieces together all possible numbers that can be used in mathematics. This includes both rational (numbers expressed as fractions or decimals) and irrational numbers (ones that cannot be expressed as a fraction or decimal).
When drawn out visually, the real number system looks like a number line. It starts on the far left side with negative infinity, and goes to the right with positive infinity. The midpoint, or the point that divides the positive and negative parts of the number line, is called the origin. This point has a value of zero.
From the origin, the numbers progress in both directions. On one side, the numbers increase from left to right and on the other side, the numbers decrease from left to right. The collection of numbers from the origin to negative infinity is known as the set of negative numbers and the collection of numbers from the origin to positive infinity is known as the set of positive numbers. Within these sets of numbers, rational and irrational numbers can be found.
In conclusion, the real number system provides a fundamental cornerstone of mathematics. Its schematic diagram gives a visual representation of the set of rational and irrational numbers, making it easier to understand. By understanding the real number system, you’ll have a better grasp of mathematics and be able to apply it to other aspects of your studies or daily life.
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