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Name: corey j catten
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995

What is a good, tangible, real-world example of a discontinuous function?

The amount of money in my checking account.


The acceleration of a typical automobile in heavy traffic.


When the domain of a function is naturally discrete then the function must be discontinuous. Good examples are tables of values. In a lottery, the probability of matching N numbers is a discrete function. When the domain is continuous, such as time or mass, etc., then a naturally discrete range (minimum gaps between units such as "cents" in asmith's account balance example) implies a discontinuous function. Another standard example is postage charges based on whole ounces even though weight is generally considered a continuous domain. Here, I must disagree with jlu's accelera- tion example. Jerky motion is not discontinuous in acceleration. For example, striking a golf ball results in a great change in its acceleration but still this occurs in some positive (small but not 0 ) time. Since we yet await our first "jump to warp speed" experience, I do not think discon- tinuous acceleration is practical in any common real model.


I am afraid that tee tries to intrude upon the idealizations of physics with irrelevant real world considerations. The fact is that we could never solve any problem if we could not idealize it. So when an ideal golf club strikes an ideal golf ball, then the club head and the ball's surface are absolutely rigid, and the acceleration of the golf ball is instantaneous. Thus, acceleration may be a discontinuous function of the time. The contrast is with position, which can never be discontinuous, otherwise a body could be in two places at the same time.


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