Experiment to prove that limits exists

[wajed]

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!)

 

[arildno]

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

 

[HallsofIvy]

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?

 

[confinement]

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.

 

[csprof2000]

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.

 

[Office_Shredder]

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.

 

[Gib Z]

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. =]