Experiment to prove that limits exists

In summary, the conversation revolves around the use of limits in mathematics and how they are an easier and more practical way to describe and model real-life situations compared to discrete measurements. It is acknowledged that measurements are never infinitely precise and that math is an approximation to real life. The example of using pi to find the area of a wooden disk is given as an illustration of the power of using limits. It is also mentioned that mathematics deals with concepts and models, not physical objects, and that it is often easier to work with these concepts rather than trying to measure and calculate exact values.
  • #1
wajed
57
0
Experiment to prove that limits exists!

1- Is this question like asking for a way to do an experiment to verify that "circles" exist?
Like, is there anything in this world that Limits can be the perfect description for (or that only limits can be the way to describe that thing)?
2- when a carpenter wants to do a table that the shape of a circle, he doesn`t mean the mathematical term "circle", but its the everyday word "circle"; well, what I mean is that the table won`t be perfectly a circle, or even have a surface that 100% has the shape of a circle. So, why do we use limits if we depend on measurements when we do things? and to be fair also, why do we also use the Idea "circle"? is it just a "standard"?


Like, why do I need to find the limit of the motion at second "2", If I`m going to need a way to measure the speed that won`t ever be perfect!

also a bank that finds the intreset of some amount of money in an infinetly small time; how would this be useful to the bank? he could just take the interest in some approximately appropriate time, (like, it wouldn`t be useful but if someone kept his money millions of years in the bank!)
 
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  • #2


How would you know that your "approximation" is, indeed, an appropriate approximation to that you wish to approximate?
 
  • #3


That's not the way mathematics works- there are no "experiments". It might well be that no "physical" circles exist but the concept does and that is what mathematics deals with.

As for 'why do I need to find the limit of the motion at second "2"', I can't answer for you (a lot of people have no such need) but I can tell you why Newton invented the calculus in order to be able to do. "Force equals mass times acceleration", acceleration is the rate of change of velocity and velocity is the rate of change of position. "Before Newton" the only way to find velocity or acceleration was to assume some change in time in order to have a change in position and velocity. But if "F= -GMm/r2", the position and so r and F, can be calculated at a specific instant. If we cannot define "velocity at a specific instant" and "acceleration at a specific instant", "ma= -GMm/r2" simply has no meaning. Newton had to invent the calculus in order to be able to assert that.

And finally, I have never heard of a bank find interest in an "infinitely small time". Where did you hear that they did?
 
  • #4


The reason we use limits is because they are much easier to work with than discrete sets of measurements taken at various time intervals. For example, to determine the area of a wooden disk it is much easier to use pi*r^2 then anything else. Similarly, the carpenter may use trigonometry to relate lengths to angles, and these functions (sine, cosine) require the notion of limits.

The point is that, after a period of study, working with limits and calculus is immensely more powerful then working with discrete measurements. Sure it's only an approximation, since there is no way to take limits experimentally, but this is irrelevant because calculus and limits justified by their practical use in describing the world.
 
  • #5


Well yeah, "physical circles" aren't "mathematical circles", and measurements are never infinitely precise.

Math is just an approximation to real life, a model, used to predict gross behavior. We need to model things because... well, measuring them is harder.
 
  • #6


I'm envisioning a high school project where you make tins one inch deep that approximate 1/sqrt(x) and 1/x near zero (up to some small epsilon away from zero) and notice that as your 1/x tin gets larger (smaller epsilon) it takes vastly more volume of water to fill the tin, whereas for the 1/sqrt(x) the increase in water needed goes to zero.
 
  • #7


csprof2000 said:
Well yeah, "physical circles" aren't "mathematical circles", and measurements are never infinitely precise.

Math is just an approximation to real life, a model, used to predict gross behavior. We need to model things because... well, measuring them is harder.

Some may prefer to think of real life as an approximation to mathematics. =]
 

FAQ: Experiment to prove that limits exists

What is the purpose of an experiment to prove that limits exist?

The purpose of this experiment is to demonstrate the concept of limits in mathematics, which is an important concept in calculus and other areas of mathematics. It helps us understand how a function behaves near a certain value and is essential in solving many real-world problems.

What materials are needed for an experiment to prove that limits exist?

The materials needed for this experiment will vary depending on the specific function being studied, but generally, you will need a graphing calculator, graph paper, a ruler, and any necessary equipment to physically manipulate the function (such as a protractor or ruler).

How do you set up an experiment to prove that limits exist?

To set up the experiment, first, choose a function to study and identify the value at which you want to find the limit. Then, graph the function and plot points near the chosen value to observe the behavior of the function. Use the graph and the points to make a prediction about the limit, and then test this prediction by finding the limit algebraically.

What are the potential sources of error in an experiment to prove that limits exist?

Some potential sources of error in this experiment include human error in plotting points or using the calculator, rounding errors in calculations, and the limitations of the graphing calculator or other equipment being used. It is important to be careful and accurate in your measurements and calculations to minimize these potential errors.

How does an experiment to prove that limits exist relate to real-world applications?

The concept of limits is used in various real-world applications such as physics, economics, and engineering. For example, in physics, limits are used to calculate the speed and acceleration of an object at a specific point in time. In economics, limits are used to determine the maximum profit or minimum cost for a given business model. Understanding limits is essential for solving problems and making predictions in these and many other fields.

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