Lecture Note
University
The University of SydneyCourse
MATH1111 | Introduction to CalculusPages
2
Academic year
7
anon
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15
Understanding the Real Line's Absolute Value Concept The collection of all real numbers is represented mathematically by the real line. The real line, as used in mathematics, is a one-dimensional numberline that displays real numbers. The real line extends in both positive andnegative directions and is continuous and unbounded. We'll get into the idea ofabsolute value, also known as magnitude, in the real line and how it's applied tofiguring out how far apart two numbers are in this article. What Is an Absolute Value? A real number's magnitude is referred to mathematically as its absolute value. A real number's magnitude is defined as its separation from zero on thereal line. The integer enclosed between two vertical lines, such as |x|, is used toexpress the absolute value of a real number. The absolute value is equal to theactual number itself if it is larger than or equal to zero. For instance, if x = 3,then |3| = 3 is x's absolute value. The absolute value is equal to the negative ofthe real number if the real number is less than zero. For instance, if x = -3, then|-3| = 3 is x's absolute value. Zero has an absolute value of zero by definition. The separation of two numbers By considering the absolute value of the difference between the two integers, one may determine the distance between two numbers on the real line.Regardless of the sequence in which the differences are obtained, this distanceequals the difference's absolute value. When x exceeds y, their separation isdenoted by x - y, which is positive and equal to the absolute value of x - y. If x isless than y, their separation is denoted as y - x, which is equivalent to theabsolute value of x - y as it is negative. A distance of zero, or the absolute valueof x - y, indicates that x and y are equal.
For instance, |4 - 2| = 2 is the absolute value of the distance between the integers, or the distance between 2 and 4. However, the distance between -2 and4 is equal to 6, which is equal to the absolute value of the disparity between thenumbers, or |4 - (-2)| = 6. Absolute value equation solving Absolute value can be utilized to solve equations in arithmetic situations where the distance between two values is predetermined. By using absolutevalue, we can utilize this equation to determine all x values that are precisely 3units apart from 2. To achieve this, keep in mind that the absolute value of thedifference between any two integers is equal to their distance from each otheron the real line. So, we may set up the equation |x - 2| = 3 to locate all x values that are precisely 3 units away from 2. Due to the fact that both numbers are 3 unitsapart from 2 in opposing directions on the real line, we thus have two potentialsolutions: x = 5 and x = -1. Calculating the separation between two integers on the real line is madepossible by the powerful mathematical concept of absolute value. In order tosolve mathematical puzzles involving distances, such as locating all x valuesthat are a specified distance from a specific integer, it is crucial to comprehendthis notion. It is important to have a firm grasp of absolute value and itsapplications in the real line whether you are a student or a professional in thearea of mathematics.
Real Line's Absolute Value Concept
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